family of ldpc codes for video broadcasting applications

ABSTRACT

A family of quasi cyclic irregular low density parity check codes for video broadcasting applications. The parity check matrices of the constructed low density parity check codes have quasi-cyclic structures to facilitate hardware implementation and have proper check/bit degree distributions to offer frame error rate performance lower than 10 −7 .

TECHNICAL FIELD OF THE INVENTION

This invention relates generally to error-correcting codes (ECC), and more particularly to a family of low-density parity-check (LDPC) codes for video broadcasting applications.

BACKGROUND OF THE INVENTION

The growth of broadband services has been fueled by consumers' demands for greater and greater data rates to support streaming video applications. Communication service providers therefore require an infrastructure that can support high data rates in bandwidth limited systems. Unfortunately, coding schemes employed in conventional video broadcasting systems can only provide relatively low throughput. Therefore, there is a need for a video broadcasting system that uses powerful LDPC codes to support higher date rates for the same bandwidth and power, without introducing greater complexity.

A fundamental problem in the field of data storage and communication is the development of efficient error-correcting codes. The mathematical foundations of error correction were established by Shannon. The most fundamental work of Shannon is the concept of noisy channel capacity, which defines a quantity that specifies the maximum rate at which information can be reliably transmitted through the channel. This capacity is called Shannon capacity. One of the most important research areas in information and coding theory is to devise coding schemes offering performance approaching Shannon capacity with reasonable complexity. Recently, a considerable interest has grown in a class of codes known as LDPC codes due to their feasible iterative decoding complexity and near-Shannon capacity performance.

In 1993, similar iterative methods were shown to perform very well for a new class of codes known as “turbo-codes.” The success of turbo-codes was partially responsible for greatly renewed interest in LDPC codes and iterative decoding methods. There has been a considerable amount of recent work to the analysis and the iterative decoding methods for both turbo-codes and LDPC codes. For instance, a special issue of the IEEE Communications Magazine was devoted to this work in August 2003 (see T. Richardson and R. Urbanke, “The Renaissance of Gallager's Low-Density Parity Check Codes,” IEEE Communications Magazine, vol. 41, pp. 126-131, August 2003, and C. Berrou, “The Ten-Year-Old Turbo Codes are entering into Service,” IEEE Communications Magazine, vol. 41, pp. 110-117, August 2003).

LDPC codes were first described by Gallager in the 1960s. LDPC codes perform remarkably close to Shannon limit. A binary (N, K) LDPC code, with a code length N and dimension K, is defined by a parity check matrix H of (N-K) rows and N columns. Most entries of the matrix H are zeros and only a small number the entries are ones, hence the matrix H is sparse. Each row of the matrix H represents a check sum, and each column represents a variable, e.g., a bit or symbol. The number of 1's in a row or a column of the parity check matrix H is called the weight of the row or the column. The LDPC codes described by Gallager are regular, i.e., the parity check matrix H has constant-weight rows and columns.

Regular LDPC codes can be extended to irregular LDPC codes, in which the weights of rows and columns vary. An irregular LDPC code is specified by degree distribution polynomials v(x) and c(x), which define the variable and check node degree distributions, respectively. More specifically, let

$\begin{matrix} {{{v(x)} = {\sum\limits_{j = 1}^{d_{v\; \max}}{v_{j}x^{j - 1}}}},{and}} & (1) \\ {{{c(x)} = {\sum\limits_{j = 1}^{d_{cmax}}{c_{j}x^{j - 1}}}},} & (2) \end{matrix}$

where the variables d_(v max) and d_(c max) are a maximum variable node degree and a check node degree, respectively, and v_(j)(c_(j)) represents the fraction of edges emanating from variable (check) nodes of degree j. The bit and check nodes degree distributions of an irregular LDPC code can also be described by specifying the numbers of bit or check nodes with different degrees. For instance, an irregular LDPC code with bit node degree distribution (b_(i),b_(j))=(N_(i),N_(j)) contains N_(i) and N_(j) bit nodes with degree b_(i) and b_(j), respectively. While irregular LDPC codes can be more complicated to represent and/or implement, it has been shown, both theoretically and empirically, that irregular LDPC codes with properly selected degree distributions outperform regular LDPC codes. FIG. 5 illustrates a parity check matrix representation of an exemplary irregular LDPC code of codeword length six.

LDPC codes can also be represented by bipartite graphs, or Tanner graphs. In a Tanner graph, one set of nodes called variable nodes (or bit nodes) corresponds to the bits of the codeword and the other set of nodes called constraints nodes (or check nodes) corresponds the set of parity check constraints which define the LDPC code. Bit nodes and check nodes are connected by edges. A bit node and a check node are to be neighbors or adjacent if they are connected by an edge. Generally, it is assumed that a pair of nodes is connected by at most one edge.

FIG. 6 illustrates a bipartite graph (Tanner graph) representation of the irregular LDPC code illustrated in FIG. 5. The LDPC code represented by FIG. 6 is of codeword length 6 and has 4 parity checks. As shown in FIG. 5, there are totally 9 one's in the parity check matrix representation of the LDPC code. Therefore in the Tanner graph representation shown in FIG. 6, 6 bit nodes 601 are connected to 4 check nodes 602 by 9 edges 603.

LDPC codes can be decoded in various ways such as majority-logic decoding and iterative decoding. Because of the structures of their parity check matrices, LDPC codes are majority-logic decodable. Although majority-logic decoding requires the least complexity and achieves reasonably good error performance for decoding some types of LDPC codes with relatively high column weights in their parity check matrices (e.g., Euclidean geometry LDPC and projective geometry LDPC codes), iterative decoding methods have received more attention due to their better performance versus complexity tradeoffs. Unlike majority-logic decoding, iterative decoding processes the received symbols recursively to improve the reliability of each symbol based on constraints that specify the code. In the first iteration, the iterative decoder only uses the channel output as input, and generates reliability output for each symbol. Subsequently, the output reliability measures of the decoded symbols at the end of each decoding iteration are used as inputs for the next iteration. The decoding process continues until a certain stopping condition is satisfied. Then final decisions are made based on the output reliability measures of the decoded symbols from the last iteration. According to the different properties of reliability measures used at each iteration, iterative decoding algorithms can be further divided into hard decision, soft decision and hybrid decision algorithms. The corresponding popular algorithms are iterative bit-flipping (BF), belief propagation (BP), and weighted bit-flipping (WBF) decoding, respectively. Since the BP algorithm has been proven to provide maximum likelihood decoding given that the underlying Tanner graph is acyclic, it becomes the most popular decoding method.

Belief propagation for LDPC codes is a type of message passing decoding. Messages transmitted along the edges of the graph are log-likelihood ratio (LLR) log p₀/p₁ associated with variable nodes corresponding to codeword bits. In this expression p₀ and p₁ denote the probability that the associated bit takes value 0 and 1, respectively. BP decoding has two steps, a horizontal step and a vertical step. In the horizontal step, each check node c_(m) sends to each adjacent bit b_(n) a check-to-bit message which is calculated based on all bit-to-check messages incoming to the check c_(m), except the one from bit b_(n). In the vertical step, each bit node b_(n) sends to each adjacent check node c_(m) a bit-to-check message which is calculated based on all check-to-bit messages incoming to the bit b_(n) except the one from check node c_(m). These two steps are repeated until a valid codeword is found or the maximum number of iterations is reached.

Because of its remarkable performance with BP decoding, irregular LDPC codes are among the best for many applications. Various irregular LDPC codes have been accepted or are being considered for various communication and storage standards, such as DVB-S2/DAB, wireline ADSL, IEEE 802.11n, and IEEE 802.16 [4][5]. While considering applying irregular LDPC codes to video broadcasting systems, one often encounters a problem related to error floor.

The error floor performance region of an LDPC decoder can be described by the error performance curve of the system. The LDPC decoder system typically exhibits a sharp decrease in error probability as the quality of the input signal improves. The resulting error performance curves are conventionally called a waterfall curve and the corresponding region is called a waterfall region. At some point, however, the decrease of error probability with input signal quality increase decreases. The resulting flat error performance curve is called the error floor. FIG. 7 illustrates an exemplary FER performance curve containing waterfall 701 and error floor regions 702 of an irregular LDPC code.

Most video broadcasting systems require a frame error rate (FER) as low as 10⁻⁷. While given codeword length of practical interest (less than 20 k) and power constraint, most irregular LDPC codes exhibit error floor higher than 10⁻⁶, which is too high for video broadcasting applications.

LDPC codes have been used in the digital video broadcasting second generation applications (DVB S2). The first generation DVBS was introduced as a standard in 1994 and is now widely used for video broadcasting throughout the world. The ECC used in DVBS is concatenated convolutional and Reed-Solomon codes which is considered not powerful enough. Therefore in 2002 DVB S2 Project called for new coding proposals which are capable of offering 30% throughput increase for the same bandwidth and power. After examining more than 7 candidates proposed by worldly renowned research labs and companies in terms of performance and hardware complexity, the committee chose a solution based on LDPC codes which provides more than 35% throughput increase with respect to DVBS. Therefore, the LDPC codes used in the DVBS2 standard are widely considered as state-of-the-art. In comparison to the LDPC codes in the DVBS2 standard, the family of LDPC codes in the present invention has two advantages. First, the codeword length of the LDPC codes in the present invention is 15360, which is much shorter than 64800, and 16200, which are the codeword lengths of the normal and the short LDPC codes in the standard DVBS2, respectively. It is well known in the ECC area that, the longer the codeword length of an LDPC code, the better the asymptotic performance the LDPC code can offer (T. Richardson, M. Shokrollahi, and R. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory, vol. 47, pp. 619-637, February 2001). Nevertheless the LDPC codes in the present invention can provide similar performance as the longer LDPC codes in the DVBS2 standard. It is also known that, from the application perspective, hardware implementation favors shorter LDPC codes which cause less design trouble and less hardware cost. The second advantage is, the LDPC codes in the present invention can offer FER lower than 10⁻⁷, which is required by video broadcasting application. By contrast, the LDPC codes in the DVBS2 standard can not provide FER lower than 10⁻⁷ by themselves therefore outer BCH codes are concatenated to the LDPC codes as outer error correcting techniques to lower the error floor. It is well known in the ECC area that, the shorter the codeword length of an LDPC code, the higher the probability the LDPC code exhibits a higher error floor. Nevertheless, without any aid of concatenated codes and with much shorter codeword length, the LDPC codes in the present invention alone can provider FER lower than 10⁻⁷.

SUMMARY OF THE INVENTION

It is an object of the invention to present a family of irregular LDPC codes with different code rates and practical codeword length which can provide error performance with error floor lower than 10⁻⁷.

The present invention is directed to irregular LDPC codes of code rates ranging from 1/4 to 9/10. The techniques of the present invention are particularly well suited for video broadcasting applications.

The LDPC codes in the present invention can offer FER performance with error floor lower than 10⁻⁷, therefore they can meet the error correcting requirements of video broadcasting applications.

At the same time, with carefully selected check and bit node degree distributions and Tanner graph constructions, the LDPC codes in the present invention have good threshold which reduce transmission power for a given FER performance.

The threshold of an LDPC code is defined as the smallest SNR value at which as the codeword length tends to infinity, the bit error probability can be made arbitrarily small.

Furthermore, the quasi-cyclic structure of the LDPC codes in the present invention simplify hardware implementation.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by way of limitation, in the figures of the corresponding drawings and in which like reference numerals refer to similar elements and in which:

FIG. 1 is an exemplary of a communications system which employs LDPC codes.

FIG. 2 illustrates an exemplary of a satellite video communications system employing LDPC codes, according to an embodiment of the present invention.

FIG. 3 illustrates an exemplary of a transmitter in FIG. 1.

FIG. 4 illustrates an exemplary of a receiver in FIG. 1.

FIG. 5 is a parity check matrix representation of an exemplary irregular LDPC code of codeword length six.

FIG. 6 illustrates a bipartite graph representation of the irregular LDPC code illustrated in FIG. 5.

FIG. 7 illustrates an exemplary FER performance curve containing waterfall and error floor regions of an irregular LDPC code.

FIG. 8 illustrates the FER performance curves of the irregular LDPC codes in the present invention.

FIG. 9 illustrates an exemplary block diagram of a video broadcasting transmitter showing a framing and LDPC encoding process transforming original user data into modulated frames, according to an embodiment of the present invention.

FIG. 10 illustrates an exemplary formed frame structure, according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The main purpose of ECC design is to construct LDPC codes with a good threshold to reduce transmission power consumption and to lower the error floor to provide satisfactory services. The main factors affecting threshold and error floor of irregular LDPC codes are check/bit distributions and Tanner graph structures. Steps involved in searching for optimal check/bit degree distributions of irregular LDPC codes will first be described. Next approaches of constructing preferable Tanner graphs based on given check/bit distributions will be discussed.

Given a code rate, irregular LDPC codes with different check/bit degree distributions have a different threshold. Good check/bit degree distributions can be searched through various optimization algorithms combined with density evolution. It has been shown that density evolution is an efficient theoretical tool to track the process of iterative message-passing decoding for LDPC codes. The idea of density evolution can be traced back to Gallager's results. To determine the performance of BF decoding, Gallager derived formulas to calculate the output BER for each iteration as a function of the input BER at the beginning of the iteration, and then iteratively calculated the BER at a given iteration. For a continuous alphabet, the calculation is more complex. The probability density functions (pdf's) of the belief messages exchanged between bit and check nodes need to be calculated from one iteration to another, and the average BER for each iteration can be derived based on these pdf's. In both check node processing and bit node processing, each outgoing belief message is a function of incoming belief messages. For a check node of degree d_(c), each outgoing message U can be expressed by a function of d_(c)−1 incoming messages,

U=F _(c)(V ₁ ,V ₂ , . . . ,V _(d) _(c) ⁻¹),

where F_(c) denotes the check node processing function which is determined from BP decoding. Similarly, for bit node of degree d_(v), each outgoing message V can be expressed by a function of d_(v)−1 incoming messages and the channel belief message U_(ch),

V=F _(v)(U _(ch) ,U ₁ ,U ₂ , . . . ,U _(d) _(v) ⁻¹),

where F_(v) denotes the bit node processing function. Although for both check and bit node processing, we can derive the pdf of an outgoing message based on the pdf's of incoming messages for a given decoding algorithm, there may exist an exponentially large number of possible formats of incoming messages. Therefore, the process of density evolution seems intractable. Fortunately, it has been proved in that for a given message-passing algorithm and noisy channel, if some symmetry conditions are satisfied, then the decoding BER is independent of the transmitted sequence x. That is to say, with the symmetry assumptions, the decoding BER of all-zero transmitted sequence x=1 is equal to that of any randomly chosen sequence. Thus, the derivation of density evolution can be considerably simplified. The symmetry conditions required by efficient density evolution are channel symmetry, check node symmetry, and bit node symmetry. Another assumption for the density evolution is that the Tanner graph is cyclic free. In that case, the incoming messages to any bit and check node are independent, and thus the derivation for the pdf of the outgoing messages can be considerably simplified. For many LDPC codes with practical interests, the corresponding Tanner graph contains cycles. Suppose the minimum length of a cycle (or girth) in a Tanner graph of an LDPC code is equal to 4×l, then the independence assumption does not hold after the l-th decoding iteration with the standard BP decoding. However, for a given iteration number, as the code length increases, the independence condition is satisfied for an increasing iteration number. Therefore, the density evolution predicts the asymptotic performance of an ensemble of LDPC codes and the “asymptotic” nature is in the sense of code length.

In order to keep the search for the optimal check/bit degree distributions of LDPC codes tractable, we let the number of types of bit nodes be four (except for rate 9/10 code which only has three types of bit nodes). For the purpose of constructing efficiently encodable irregular LDPC codes with good threshold, we let the number of bit nodes with degree two be (N_(s)−K_(s)−1)×S, where S=32 is a constant, and N_(s)=N/S, K_(s)=K/S. For each code rate R, the message length can be calculated as K=N×R, where N=15360. Let d_(v,x)×S be the number of bit nodes with degree x. Given each R, for d_(v,3)=1, . . . ,K_(s)+1 and d_(v,4)=0, . . . ,K_(s), we can determine the number of the bit node with largest weight d_(v,max)=K_(s)+1−d_(v,3)−d_(v,4). Then we can search for the optimal check/bit degree distributions with the smallest threshold for each d_(v,3). Finally among the check/bit degree distributions associated with LDPC codes having an error floor lower than 10⁻⁷ and codeword length N=15360, we select the one with the smallest threshold. Table 1 lists the check/bit degree distributions for irregular LDPC codes with code rate 1/4, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 13/15, and 9/10.

TABLE 1 Bit node degree distributions bit rate 2 3 4 6 7 10 12 ¼ 11264 256 3840 ⅖ 8960 256 4608 1536 ½ 7424 2304 3840 1792 ⅗ 5888 3328 4352 1792 ⅔ 4864 4096 4864 1536 ¾ 3584 4608 5888 1280 ⅘ 2816 5888 5376 1280 ⅚ 2304 4608 6912 1536 13/15 1792 5632 6912 1024   9/10 1280 3584 10496

Given the check/bit degree distributions, an LDPC code can be constructed in several methods. These methods can be decomposed into two main classes, random or pseudorandom constructions, and algebraic constructions. Since the special structure of algebraic LDPC codes greatly facilitate the hardware implementation of decoders, we consider algebraic constructions. Algebraic constructions of LDPC codes can be further decomposed into two main categories. The first category is based on finite geometries while the second category is based on cyclic shift matrices. Because of the flexible parameters of cyclic-shift-based LDPC codes, we consider LDPC codes constructed based on circulant permutation matrices. The parity check matrix of a quasi-cyclic LDPC code is expanded from a base matrix associated with shift numbers. Given check/bit degree distributions, the ultimate performance of an LDPC code decoded by the BP algorithm mainly depends on the smallest length of loops in the corresponding Tanner graph, which is called girth. The girth of a quasi-cyclic LDPC codes is determined by the girth of the Tanner graph of the based matrix and the shift numbers. Conventionally, the Tanner graph of the base matrix first optimized based on the check/bit degree distributions, then optimal shift values are assigned to entries of the base matrix. According to a method of the invention for constructing quasi-cyclic LDPC codes, the Tanner graph of the base matrix and the shift values are optimized simultaneously.

It should be understood that the following specification may be performed or stored on a readable storage media, computer software, or hardware, such as storage tapes, RAM, ROM, flash memory, synthesized logic as is well known in the art.

In the present invention, each LDPC code is defined by a binary parity check matrix H of size (N−K)×N, which is expanded from a base matrix B of size

$\left( \frac{N - K}{32} \right) \times {\left( \frac{N}{32} \right).}$

The base matrix defining (through expanded to parity check matrix) each LDPC code in the present invention is specified by the specification in the appendix. Each specification of the base matrix contains groups of numbers and each group contains 3 numbers. Each group of 3 numbers i j k specifies a non-negative entry of base matrix B, i.e, B_(i,j)=k. For instance, Table A of the Appendix is the specification of B_(1/4) which defines the base matrix B for the rate-1/4 LDPC code and the first group 0 16 9 denotes B_(0,16)=9. All the entries not specified in the corresponding table are assigned with value −1. The parity check matrix H is expanded from B by replacing each non-negative entry B_(i,j) with a B_(i,j)-right-shifted identity matrix of size 32×32, and each negative entry with an all-zero matrix of size 32×32. A B_(i,j)-right-shifted identity matrix is a circulant permutation matrix with a 1 at column-(r+B_(i,j))mod32 for row-r, 0≦r≦31, and zero elsewhere. All the LDPC codes in the present invention have codeword length 15360, therefore the parity check matrix H of the LDPC code with rate R contains 15360×(1−R) rows and 15360 columns.

LDPC codes in the present invention are linear block codes. Once the parity check matrix H of size (N−K)×N is specified, an LDPC code with codeword length N and dimension K is uniquely defined by H. Exchanging among any rows of parity check matrix H results in a new parity check matrix H′, which is called permutation of H. The LDPC code defined by a parity check matrix H is the same LDPC code defined by the permutation of the parity check matrix H. Therefore when we refer to an LDPC code defined by a parity check matrix H, we refer to an equivalent LDPC code defined by any possible permutation of H. Besides permutation of parity check matrix H, there exists many other ways to define or describe the LDPC code defined by H. When we refer to an LDPC code defined by a parity check matrix H, we refer to an equivalent LDPC code described in any format.

FIG. 1 is a diagram of a communications system employing LDPC codes, according to an embodiment of the present invention. A communications system includes a transmitter 101 which generates signal waveforms across a communication channel 102 to a receiver 103. The transmitter 101 contains a message source producing a discrete set of possible messages and each of these messages corresponds a signal waveform. The waveforms enter the channel 102 and is corrupted by noise. LDPC codes are employed to reduce the disturbances introduced by the channel 102.

FIG. 2 depicts a diagram of a video broadcasting system using LDPC codes, according to an embodiment of the present inversion. The satellite 201 broadcasts video program from the hub station 202 to the satellite terminals 203, which may include a set top box 204 for interfacing with a television display 205. In direct video broadcasting applications, power and bandwidth efficiency are essential. In the conventional video broadcasting systems, ECC techniques such as turbo trellis coding are used to provide power and bandwidth efficiency. Nevertheless the conventional ECC techniques require higher complexity and offer low throughput given power constraint. On the contrast, LDPC codes can offer high power and bandwidth efficiency without increased complexity. What is more, the structures of LDPC codes make them essentially suitable for parallel decoding which can greatly reduce decoding delay.

FIG. 3 depicts an exemplary transmitter in the communications system of FIG. 1 which employs LDPC codes as ECC. The LDPC encoder 302 encodes information bits from source 301 into LDPC codewords. The mapping from each information block to each LDPC codeword is specified by the parity check matrix (or equivalently the generator matrix) of the LDPC code. The LDPC codeword is interleaved (for some communication systems) and modulated to signal waveforms by the interleaver/modulator 303. These signal waveforms are sent to a transmit antenna 304 and propagated to a receiver shown in FIG. 4.

FIG. 4 depicts an exemplary receiver in FIG. 1 which employs LDPC codes as ECC. Signal waveforms are received by the receiving antenna 401 and distributed to demodulator/deinterleaveror 402. Signal waveforms are demodulated by demodulator and deinterleaved by deinterleavor (for some communication systems) and then distributed to a LDPC decoder 403 which iteratively decodes the received messages and output estimations of the transmitted codeword.

For most video broadcasting systems, directly transmitting an LDPC encoded and modulated signal waveforms is not acceptable, because receivers can't decode received signals without knowing where each encoded LDPC codeword starts or ends. Time references (or markers) therefore haven been necessary throughout the transmission to help identify the positions of LDPC codewords. Similarly, typical communication systems require that receiver's time and frequency be locked to a transmitter's reference, which is referred to as synchronization.

Furthermore, certain overhead information is typically periodically transferred to enable receivers to properly demodulate transmitted signals, decode signals and abstract user messages. For at least these reasons, typical transmitters insert a synchronization pattern and a header periodically into encoded messages, a process called frame formatting. Typically, a receiver first tries to lock onto a synchronization pattern and then decodes the header and message signal. Frame formatting design is critical to overall system performance and can directly impact the cost of establishing and operating a communication system. Frame formatting design often depends on many factors, such as channel characteristics, modulation type and ECC scheme. A well designed frame format may result in high performance receivers that achieve fast frame acquisition, reliable tracking (time and frequency lock) and improved ECC decoding performance (such as meeting the required FER) with minimum overhead at a low cost.

FIG. 9 illustrates an exemplary block diagram of a video broadcasting transmitter showing a framing and LDPC encoding process transforming original user data into modulated frames, according to an embodiment of the present invention. Through a process of frame grouping 901, the input data bits to be transmitted are first divided into subsequent groups, e.g. group n and group n+1. Each group contains a number of information bits required for the corresponding frame. Each of the information groups is then prefixed by a header (H) by the header insertion module 902. The header, along with each group, is further divided into j (an integer) sub-groups (sg) by the codeword grouping module 903, with each sub-group carrying an equal number of bits. For illustration purpose, j denotes the number of sub-groups in each group. For each sub-group, in an LDPC encoding 904 process, an LDPC encoder computes the error checking and error correction parity bits (P) of a fixed length based on the sub-group's data pattern and attaches the parity bits to the end of the associated sub-group to form a code word. Then the symbol mapping module 905 maps the bit stream of each codeword into modulation symbols according to the corresponding modulation type in the codeword. Following the symbol mapping, all frames are of an equal length, regardless of modulation used. Next the pilot insertion module 906 may insert a number of pilot waves (p) evenly into the encoded frames as shown in FIG. 1. Also, the UW and ACC insertion module 907 will add a UW followed by an ACC at the beginning of each frame. The symbol scrambler 908 scrambles the symbols of each frame except the UW using a fixed scrambling pattern. Finally, all the symbols may be modulated by modulator 909 to a radio frequency for transmission through an antenna.

FIG. 10 depicts an exemplary frame format of a transmitted frame containing encoded LDPC codewords according to an embodiment of the present invention. The frame starts with an 64-symbol unique word 1001, followed by 64-symbol auxiliary control code 1002, and m+1 segments 1003 of encoded LDPC data (or payload data) separated by m evenly distributed pilots 1004.

FIG. 8 depicts the performance of the family of quasi-cyclic irregular LDPC codes of code rate 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 13/15, and 9/10. From the simulation results, we observe that all codes have error floor lower than 10⁻⁷ and exhibit good threshold.

Appendix Tables A-J are specifications of the base matrices B for the code rates of 1/4, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 13/15, and 9/10, respectively.

Although the invention has been described by the way of examples of preferred embodiments, it is to be understood that various other adaptations and modifications may be made within the spirit and scope of the invention. Therefore, it is the object of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the invention.

APPENDIX

APPENDIX TABLE A Specification of the base matrix B_(1/4) for the rate-¼ LDPC code 0 61 9 0 119 21 0 120 0 0 128 0 1 47 0 1 103 6 1 165 0 1 173 0 2 30 1 2 113 0 2 210 0 2 218 0 3 23 21 3 86 17 3 255 0 3 263 0 4 0 7 4 60 5 4 125 0 4 300 0 4 308 0 5 38 3 5 70 20 5 345 0 5 353 0 6 9 2 6 76 7 6 390 0 6 398 0 7 7 18 7 108 14 7 435 0 7 443 0 8 62 9 8 112 22 8 121 0 8 129 0 9 40 1 9 96 7 9 166 0 9 174 0 10 31 1 10 114 0 10 211 0 10 219 0 11 5 31 11 30 30 11 119 22 11 256 0 11 264 0 12 1 7 12 61 5 12 126 0 12 301 0 12 309 0 13 39 3 13 71 20 13 346 0 13 354 0 14 10 2 14 77 7 14 391 0 14 399 0 15 0 19 15 109 14 15 436 0 15 444 0 16 63 9 16 113 22 16 122 0 16 130 0 17 41 1 17 97 7 17 167 0 17 175 0 18 24 2 18 115 0 18 212 0 18 220 0 19 6 31 19 31 30 19 112 23 19 257 0 19 265 0 20 2 7 20 62 5 20 127 0 20 302 0 20 310 0 21 32 4 21 64 21 21 347 0 21 355 0 22 4 1 22 114 7 22 392 0 22 400 0 23 1 19 23 110 14 23 437 0 23 445 0 24 56 10 24 114 22 24 123 0 24 131 0 25 37 16 25 94 31 25 168 0 25 176 0 26 25 2 26 116 0 26 213 0 26 221 0 27 7 31 27 24 31 27 113 23 27 258 0 27 266 0 28 3 7 28 63 5 28 120 1 28 303 0 28 311 0 29 33 4 29 65 21 29 348 0 29 356 0 30 5 1 30 115 7 30 393 0 30 401 0 31 2 19 31 111 14 31 438 0 31 446 0 32 57 10 32 115 22 32 124 0 32 132 0 33 38 16 33 95 31 33 169 0 33 177 0 34 26 2 34 117 0 34 214 0 34 222 0 35 0 0 35 25 31 35 114 23 35 259 0 35 267 0 36 45 2 36 85 30 36 304 0 36 312 0 37 34 4 37 66 21 37 349 0 37 357 0 38 6 1 38 116 7 38 394 0 38 402 0 39 3 19 39 104 15 39 439 0 39 447 0 40 58 10 40 116 22 40 125 0 40 133 0 41 39 16 41 88 0 41 170 0 41 178 0 42 27 2 42 118 0 42 215 0 42 223 0 43 1 0 43 26 31 43 115 23 43 260 0 43 268 0 44 46 2 44 86 30 44 305 0 44 313 0 45 35 4 45 67 21 45 350 0 45 358 0 46 7 1 46 117 7 46 395 0 46 403 0 47 28 16 47 106 31 47 440 0 47 448 0 48 59 10 48 117 22 48 126 0 48 134 0 49 32 17 49 89 0 49 171 0 49 179 0 50 21 23 50 76 25 50 216 0 50 224 0 51 2 0 51 27 31 51 116 23 51 261 0 51 269 0 52 47 2 52 87 30 52 306 0 52 314 0 53 36 4 53 68 21 53 351 0 53 359 0 54 0 2 54 118 7 54 396 0 54 404 0 55 29 16 55 107 31 55 441 0 55 449 0 56 60 10 56 118 22 56 127 0 56 135 0 57 33 17 57 90 0 57 172 0 57 180 0 58 22 23 58 77 25 58 217 0 58 225 0 59 3 0 59 28 31 59 117 23 59 262 0 59 270 0 60 40 3 60 80 31 60 307 0 60 315 0 61 30 22 61 112 4 61 352 0 61 360 0 62 1 2 62 119 7 62 397 0 62 405 0 63 30 16 63 108 31 63 442 0 63 450 0 64 59 2 64 111 21 64 128 0 64 136 0 65 34 17 65 91 0 65 173 0 65 181 0 66 23 23 66 78 25 66 218 0 66 226 0 67 4 0 67 29 31 67 118 23 67 263 0 67 271 0 68 41 3 68 81 31 68 308 0 68 316 0 69 31 22 69 113 4 69 353 0 69 361 0 70 2 2 70 112 8 70 398 0 70 406 0 71 31 16 71 109 31 71 443 0 71 451 0 72 60 2 72 104 22 72 129 0 72 137 0 73 35 17 73 92 0 73 174 0 73 182 0 74 16 24 74 79 25 74 219 0 74 227 0 75 33 4 75 64 6 75 264 0 75 272 0 76 42 3 76 82 31 76 309 0 76 317 0 77 24 23 77 114 4 77 354 0 77 362 0 78 3 2 78 113 8 78 399 0 78 407 0 79 24 17 79 110 31 79 444 0 79 452 0 80 61 2 80 105 22 80 130 0 80 138 0 81 36 17 81 93 0 81 175 0 81 183 0 82 17 24 82 72 26 82 220 0 82 228 0 83 34 4 83 65 6 83 265 0 83 273 0 84 43 3 84 83 31 84 310 0 84 318 0 85 25 23 85 115 4 85 355 0 85 363 0 86 19 3 86 61 4 86 400 0 86 408 0 87 25 17 87 111 31 87 445 0 87 453 0 88 62 2 88 106 22 88 131 0 88 139 0 89 40 15 89 114 11 89 176 0 89 184 0 90 18 24 90 73 26 90 221 0 90 229 0 91 35 4 91 66 6 91 266 0 91 274 0 92 44 3 92 84 31 92 311 0 92 319 0 93 26 23 93 116 4 93 356 0 93 364 0 94 20 3 94 62 4 94 401 0 94 409 0 95 26 17 95 104 0 95 446 0 95 454 0 96 63 2 96 107 22 96 132 0 96 140 0 97 41 15 97 115 11 97 177 0 97 185 0 98 19 24 98 74 26 98 222 0 98 230 0 99 36 4 99 67 6 99 267 0 99 275 0 100 9 11 100 65 2 100 312 0 100 320 0 101 27 23 101 117 4 101 357 0 101 365 0 102 21 3 102 63 4 102 402 0 102 410 0 103 27 17 103 105 0 103 447 0 103 455 0 104 56 3 104 108 22 104 133 0 104 141 0 105 42 15 105 116 11 105 178 0 105 186 0 106 20 24 106 75 26 106 223 0 106 231 0 107 37 4 107 68 6 107 268 0 107 276 0 108 10 11 108 66 2 108 313 0 108 321 0 109 28 23 109 118 4 109 358 0 109 366 0 110 22 3 110 56 5 110 403 0 110 411 0 111 72 5 111 448 0 111 456 0 112 57 3 112 109 22 112 134 0 112 142 0 113 43 15 113 117 11 113 179 0 113 187 0 114 49 1 114 96 24 114 224 0 114 232 0 115 38 4 115 69 6 115 269 0 115 277 0 116 11 11 116 67 2 116 314 0 116 322 0 117 29 23 117 119 4 117 359 0 117 367 0 118 23 3 118 57 5 118 404 0 118 412 0 119 73 5 119 449 0 119 457 0 120 58 3 120 110 22 120 135 0 120 143 0 121 44 15 121 118 11 121 180 0 121 188 0 122 50 1 122 97 24 122 225 0 122 233 0 123 39 4 123 70 6 123 270 0 123 278 0 124 12 11 124 68 2 124 315 0 124 323 0 125 39 25 125 64 16 125 360 0 125 368 0 126 16 4 126 58 5 126 405 0 126 413 0 127 74 5 127 450 0 127 458 0 128 58 8 128 108 7 128 136 0 128 144 0 129 45 15 129 119 11 129 181 0 129 189 0 130 51 1 130 98 24 130 226 0 130 234 0 131 32 5 131 71 6 131 271 0 131 279 0 132 13 11 132 69 2 132 316 0 132 324 0 133 32 26 133 65 16 133 361 0 133 369 0 134 17 4 134 59 5 134 406 0 134 414 0 135 75 5 135 451 0 135 459 0 136 59 8 136 109 7 136 137 0 136 145 0 137 46 15 137 112 12 137 182 0 137 190 0 138 52 1 138 99 24 138 227 0 138 235 0 139 36 20 139 95 14 139 272 0 139 280 0 140 14 11 140 70 2 140 317 0 140 325 0 141 33 26 141 66 16 141 362 0 141 370 0 142 18 4 142 60 5 142 407 0 142 415 0 143 76 5 143 452 0 143 460 0 144 60 8 144 110 7 144 138 0 144 146 0 145 47 15 145 113 12 145 183 0 145 191 0 146 53 1 146 100 24 146 228 0 146 236 0 147 37 20 147 88 15 147 273 0 147 281 0 148 15 11 148 71 2 148 318 0 148 326 0 149 34 26 149 67 16 149 363 0 149 371 0 150 23 31 150 90 4 150 408 0 150 416 0 151 77 5 151 453 0 151 461 0 152 61 8 152 111 7 152 139 0 152 147 0 153 45 14 153 82 31 153 184 0 153 192 0 154 54 1 154 101 24 154 229 0 154 237 0 155 38 20 155 89 15 155 274 0 155 282 0 156 8 12 156 64 3 156 319 0 156 327 0 157 35 26 157 68 16 157 364 0 157 372 0 158 16 0 158 91 4 158 409 0 158 417 0 159 78 5 159 454 0 159 462 0 160 62 8 160 104 8 160 140 0 160 148 0 161 46 14 161 83 31 161 185 0 161 193 0 162 55 1 162 102 24 162 230 0 162 238 0 163 39 20 163 90 15 163 275 0 163 283 0 164 21 23 164 97 25 164 320 0 164 328 0 165 36 26 165 69 16 165 365 0 165 373 0 166 17 0 166 92 4 166 410 0 166 418 0 167 79 5 167 455 0 167 463 0 168 63 8 168 105 8 168 141 0 168 149 0 169 47 14 169 84 31 169 186 0 169 194 0 170 48 2 170 103 24 170 231 0 170 239 0 171 32 21 171 91 15 171 276 0 171 284 0 172 22 23 172 98 25 172 321 0 172 329 0 173 37 26 173 70 16 173 366 0 173 374 0 174 18 0 174 93 4 174 411 0 174 419 0 175 19 15 175 87 24 175 456 0 175 464 0 176 56 9 176 106 8 176 142 0 176 150 0 177 40 15 177 85 31 177 187 0 177 195 0 178 26 5 178 99 7 178 232 0 178 240 0 179 33 21 179 92 15 179 277 0 179 285 0 180 23 23 180 99 25 180 322 0 180 330 0 181 38 26 181 71 16 181 367 0 181 375 0 182 19 0 182 94 4 182 412 0 182 420 0 183 20 15 183 80 25 183 457 0 183 465 0 184 57 9 184 107 8 184 143 0 184 151 0 185 41 15 185 86 31 185 188 0 185 196 0 186 27 5 186 100 7 186 233 0 186 241 0 187 34 21 187 93 15 187 278 0 187 286 0 188 16 24 188 100 25 188 323 0 188 331 0 189 47 22 189 96 18 189 368 0 189 376 0 190 20 0 190 95 4 190 413 0 190 421 0 191 21 15 191 81 25 191 458 0 191 466 0 192 52 22 192 107 22 192 144 0 192 152 0 193 42 15 193 87 31 193 189 0 193 197 0 194 28 5 194 101 7 194 234 0 194 242 0 195 35 21 195 94 15 195 279 0 195 287 0 196 17 24 196 101 25 196 324 0 196 332 0 197 40 23 197 97 18 197 369 0 197 377 0 198 21 0 198 88 5 198 414 0 198 422 0 199 22 15 199 82 25 199 459 0 199 467 0 200 53 22 200 108 22 200 145 0 200 153 0 201 43 15 201 80 0 201 190 0 201 198 0 202 29 5 202 102 7 202 235 0 202 243 0 203 39 23 203 94 23 203 280 0 203 288 0 204 18 24 204 102 25 204 325 0 204 333 0 205 41 23 205 98 18 205 370 0 205 378 0 206 22 0 206 89 5 206 415 0 206 423 0 207 23 15 207 83 25 207 460 0 207 468 0 208 54 22 208 109 22 208 146 0 208 154 0 209 44 15 209 81 0 209 191 0 209 199 0 210 30 5 210 103 7 210 236 0 210 244 0 211 32 24 211 95 23 211 281 0 211 289 0 212 19 24 212 103 25 212 326 0 212 334 0 213 42 23 213 99 18 213 371 0 213 379 0 214 15 19 214 69 26 214 416 0 214 424 0 215 16 16 215 84 25 215 461 0 215 469 0 216 55 22 216 110 22 216 147 0 216 155 0 217 53 23 217 90 18 217 192 0 217 200 0 218 31 5 218 96 8 218 237 0 218 245 0 219 33 24 219 88 24 219 282 0 219 290 0 220 20 24 220 96 26 220 327 0 220 335 0 221 43 23 221 100 18 221 372 0 221 380 0 222 8 20 222 70 26 222 417 0 222 425 0 223 17 16 223 85 25 223 462 0 223 470 0 224 48 23 224 111 22 224 148 0 224 156 0 225 54 23 225 91 18 225 193 0 225 201 0 226 24 6 226 97 8 226 238 0 226 246 0 227 34 24 227 89 24 227 283 0 227 291 0 228 3 0 228 96 13 228 328 0 228 336 0 229 44 23 229 101 18 229 373 0 229 381 0 230 9 20 230 71 26 230 418 0 230 426 0 231 18 16 231 86 25 231 463 0 231 471 0 232 49 23 232 104 23 232 149 0 232 157 0 233 55 23 233 92 18 233 194 0 233 202 0 234 25 6 234 98 8 234 239 0 234 247 0 235 35 24 235 90 24 235 284 0 235 292 0 236 4 0 236 97 13 236 329 0 236 337 0 237 45 23 237 102 18 237 374 0 237 382 0 238 10 20 238 64 27 238 419 0 238 427 0 239 15 29 239 83 20 239 464 0 239 472 0 240 50 23 240 105 23 240 150 0 240 158 0 241 48 24 241 93 18 241 195 0 241 203 0 242 13 16 242 73 24 242 240 0 242 248 0 243 36 24 243 91 24 243 285 0 243 293 0 244 5 0 244 98 13 244 330 0 244 338 0 245 46 23 245 103 18 245 375 0 245 383 0 246 11 20 246 65 27 246 420 0 246 428 0 247 8 30 247 84 20 247 465 0 247 473 0 248 51 23 248 106 23 248 151 0 248 159 0 249 49 24 249 94 18 249 196 0 249 204 0 250 14 16 250 74 24 250 241 0 250 249 0 251 37 24 251 92 24 251 286 0 251 294 0 252 6 0 252 99 13 252 331 0 252 339 0 253 41 23 253 80 16 253 376 0 253 384 0 254 12 20 254 66 27 254 421 0 254 429 0 255 9 30 255 85 20 255 466 0 255 474 0 256 54 20 256 106 9 256 152 0 256 160 0 257 50 24 257 95 18 257 197 0 257 205 0 258 15 16 258 75 24 258 242 0 258 250 0 259 38 24 259 93 24 259 287 0 259 295 0 260 7 0 260 100 13 260 332 0 260 340 0 261 42 23 261 81 16 261 377 0 261 385 0 262 13 20 262 67 27 262 422 0 262 430 0 263 10 30 263 86 20 263 467 0 263 475 0 264 55 20 264 107 9 264 153 0 264 161 0 265 51 24 265 88 19 265 198 0 265 206 0 266 8 17 266 76 24 266 243 0 266 251 0 267 8 0 267 64 0 267 288 0 267 296 0 268 0 1 268 101 13 268 333 0 268 341 0 269 43 23 269 82 16 269 378 0 269 386 0 270 14 20 270 68 27 270 423 0 270 431 0 271 11 30 271 87 20 271 468 0 271 476 0 272 48 21 272 108 9 272 154 0 272 162 0 273 52 24 273 89 19 273 199 0 273 207 0 274 9 17 274 77 24 274 244 0 274 252 0 275 9 0 275 65 0 275 289 0 275 297 0 276 1 1 276 102 13 276 334 0 276 342 0 277 44 23 277 83 16 277 379 0 277 387 0 278 54 6 278 75 21 278 424 0 278 432 0 279 12 30 279 80 21 279 469 0 279 477 0 280 49 21 280 109 9 280 155 0 280 163 0 281 29 21 281 88 29 281 200 0 281 208 0 282 10 17 282 78 24 282 245 0 282 253 0 283 10 0 283 66 0 283 290 0 283 298 0 284 2 1 284 103 13 284 335 0 284 343 0 285 45 23 285 84 16 285 380 0 285 388 0 286 55 6 286 76 21 286 425 0 286 433 0 287 13 30 287 81 21 287 470 0 287 478 0 288 50 21 288 110 9 288 156 0 288 164 0 289 30 21 289 89 29 289 201 0 289 209 0 290 11 17 290 79 24 290 246 0 290 254 0 291 11 0 291 67 0 291 291 0 291 299 0 292 52 14 292 77 7 292 336 0 292 344 0 293 46 23 293 85 16 293 381 0 293 389 0 294 48 7 294 77 21 294 426 0 294 434 0 295 14 30 295 82 21 295 471 0 295 479 0 296 51 21 296 111 9 296 157 0 296 165 0 297 31 21 297 90 29 297 202 0 297 210 0 298 12 17 298 72 25 298 247 0 298 255 0 299 12 0 299 68 0 299 292 0 299 300 0 300 53 14 300 78 7 300 337 0 300 345 0 301 47 23 301 86 16 301 382 0 301 390 0 302 49 7 302 78 21 302 427 0 302 435 0 303 7 4 303 60 26 303 122 0 303 472 0 304 52 21 304 104 10 304 158 0 304 166 0 305 24 22 305 91 29 305 203 0 305 211 0 306 16 21 306 87 16 306 248 0 306 256 0 307 13 0 307 69 0 307 293 0 307 301 0 308 54 14 308 79 7 308 338 0 308 346 0 309 40 24 309 87 16 309 383 0 309 391 0 310 50 7 310 79 21 310 428 0 310 436 0 311 0 5 311 61 26 311 123 0 311 473 0 312 53 21 312 105 10 312 159 0 312 167 0 313 25 22 313 92 29 313 204 0 313 212 0 314 17 21 314 80 17 314 249 0 314 257 0 315 14 0 315 70 0 315 294 0 315 302 0 316 55 14 316 72 8 316 339 0 316 347 0 317 11 1 317 78 6 317 384 0 317 392 0 318 51 7 318 72 22 318 429 0 318 437 0 319 1 5 319 62 26 319 124 0 319 474 0 320 42 0 320 98 6 320 160 0 320 168 0 321 26 22 321 93 29 321 205 0 321 213 0 322 18 21 322 81 17 322 250 0 322 258 0 323 15 0 323 71 0 323 295 0 323 303 0 324 48 15 324 73 8 324 340 0 324 348 0 325 12 1 325 79 6 325 385 0 325 393 0 326 52 7 326 73 22 326 430 0 326 438 0 327 2 5 327 63 26 327 125 0 327 475 0 328 43 0 328 99 6 328 161 0 328 169 0 329 27 22 329 94 29 329 206 0 329 214 0 330 19 21 330 82 17 330 251 0 330 259 0 331 4 6 331 56 5 331 121 0 331 296 0 331 304 0 332 49 15 332 74 8 332 341 0 332 349 0 333 13 1 333 72 7 333 386 0 333 394 0 334 53 7 334 74 22 334 431 0 334 439 0 335 3 5 335 56 27 335 126 0 335 476 0 336 44 0 336 100 6 336 162 0 336 170 0 337 28 22 337 95 29 337 207 0 337 215 0 338 20 21 338 83 17 338 252 0 338 260 0 339 5 6 339 57 5 339 122 0 339 297 0 339 305 0 340 50 15 340 75 8 340 342 0 340 350 0 341 14 1 341 73 7 341 387 0 341 395 0 342 4 18 342 105 14 342 432 0 342 440 0 343 4 5 343 57 27 343 127 0 343 477 0 344 45 0 344 101 6 344 163 0 344 171 0 345 28 1 345 119 31 345 208 0 345 216 0 346 21 21 346 84 17 346 253 0 346 261 0 347 6 6 347 58 5 347 123 0 347 298 0 347 306 0 348 51 15 348 76 8 348 343 0 348 351 0 349 15 1 349 74 7 349 388 0 349 396 0 350 5 18 350 106 14 350 433 0 350 441 0 351 5 5 351 58 27 351 120 1 351 478 0 352 46 0 352 102 6 352 164 0 352 172 0 353 29 1 353 112 0 353 209 0 353 217 0 354 22 21 354 85 17 354 254 0 354 262 0 355 7 6 355 59 5 355 124 0 355 299 0 355 307 0 356 37 3 356 69 20 356 344 0 356 352 0 357 8 2 357 75 7 357 389 0 357 397 0 358 6 18 358 107 14 358 434 0 358 442 0 359 6 5 359 59 27 359 121 1 359 479 0

APPENDIX TABLE B Specification the base matrix B_(2/5) for the rate-⅖ LDPC code 0 18 12 0 42 1 0 113 18 0 184 9 0 192 0 0 200 0 1 12 23 1 37 20 1 97 29 1 175 13 1 228 0 1 236 0 2 10 6 2 39 3 2 96 6 2 149 18 2 264 0 2 272 0 3 12 11 3 40 3 3 72 28 3 182 8 3 300 0 3 308 0 4 19 29 4 45 18 4 87 20 4 193 0 4 336 0 4 344 0 5 19 16 5 28 26 5 61 11 5 186 14 5 372 0 5 380 0 6 7 13 6 47 0 6 58 11 6 191 16 6 408 0 6 416 0 7 22 20 7 52 27 7 108 23 7 170 24 7 444 0 7 452 0 8 19 12 8 43 1 8 114 18 8 185 9 8 193 0 8 201 0 9 13 23 9 38 20 9 98 29 9 168 14 9 229 0 9 237 0 10 11 6 10 32 4 10 97 6 10 150 18 10 265 0 10 273 0 11 13 11 11 41 3 11 73 28 11 183 8 11 301 0 11 309 0 12 20 29 12 46 18 12 80 21 12 194 0 12 337 0 12 345 0 13 20 16 13 29 26 13 62 11 13 187 14 13 373 0 13 381 0 14 0 14 14 40 1 14 59 11 14 184 17 14 409 0 14 417 0 15 23 20 15 53 27 15 109 23 15 171 24 15 445 0 15 453 0 16 20 12 16 44 1 16 115 18 16 186 9 16 194 0 16 202 0 17 14 23 17 39 20 17 99 29 17 169 14 17 230 0 17 238 0 18 12 6 18 33 4 18 98 6 18 151 18 18 266 0 18 274 0 19 14 11 19 42 3 19 74 28 19 176 9 19 302 0 19 310 0 20 21 29 20 47 18 20 81 21 20 195 0 20 338 0 20 346 0 21 21 16 21 30 26 21 63 11 21 188 14 21 374 0 21 382 0 22 1 14 22 41 1 22 60 11 22 185 17 22 410 0 22 418 0 23 16 21 23 54 27 23 110 23 23 172 24 23 446 0 23 454 0 24 21 12 24 45 1 24 116 18 24 187 9 24 195 0 24 203 0 25 15 23 25 32 21 25 100 29 25 170 14 25 231 0 25 239 0 26 13 6 26 34 4 26 99 6 26 144 19 26 267 0 26 275 0 27 15 11 27 43 3 27 75 28 27 177 9 27 303 0 27 311 0 28 22 29 28 40 19 28 82 21 28 196 0 28 339 0 28 347 0 29 22 16 29 31 26 29 56 12 29 189 14 29 375 0 29 383 0 30 2 14 30 42 1 30 61 11 30 186 17 30 411 0 30 419 0 31 17 21 31 55 27 31 111 23 31 173 24 31 447 0 31 455 0 32 22 12 32 46 1 32 117 18 32 188 9 32 196 0 32 204 0 33 5 14 33 27 4 33 119 11 33 162 29 33 232 0 33 240 0 34 14 6 34 35 4 34 100 6 34 145 19 34 268 0 34 276 0 35 6 20 35 24 0 35 115 1 35 138 29 35 304 0 35 312 0 36 23 29 36 41 19 36 83 21 36 197 0 36 340 0 36 348 0 37 12 24 37 37 23 37 99 26 37 134 26 37 376 0 37 384 0 38 3 14 38 43 1 38 62 11 38 187 17 38 412 0 38 420 0 39 8 29 39 24 1 39 66 10 39 128 25 39 448 0 39 456 0 40 23 12 40 47 1 40 118 18 40 189 9 40 197 0 40 205 0 41 6 14 41 28 4 41 112 12 41 163 29 41 233 0 41 241 0 42 15 6 42 36 4 42 101 6 42 146 19 42 269 0 42 277 0 43 7 20 43 25 0 43 116 1 43 139 29 43 305 0 43 313 0 44 16 30 44 42 19 44 84 21 44 198 0 44 341 0 44 349 0 45 13 24 45 38 23 45 100 26 45 135 26 45 377 0 45 385 0 46 4 14 46 44 1 46 63 11 46 188 17 46 413 0 46 421 0 47 9 29 47 25 1 47 67 10 47 129 25 47 449 0 47 457 0 48 16 13 48 40 2 48 119 18 48 190 9 48 198 0 48 206 0 49 7 14 49 29 4 49 113 12 49 164 29 49 234 0 49 242 0 50 8 7 50 37 4 50 102 6 50 147 19 50 270 0 50 278 0 51 0 21 51 26 0 51 117 1 51 140 29 51 306 0 51 314 0 52 17 30 52 43 19 52 85 21 52 199 0 52 342 0 52 350 0 53 14 24 53 39 23 53 101 26 53 128 27 53 378 0 53 386 0 54 5 14 54 45 1 54 56 12 54 189 17 54 414 0 54 422 0 55 10 29 55 26 1 55 68 10 55 130 25 55 450 0 55 458 0 56 17 13 56 41 2 56 112 19 56 191 9 56 199 0 56 207 0 57 0 15 57 30 4 57 114 12 57 165 29 57 235 0 57 243 0 58 9 7 58 38 4 58 103 6 58 148 19 58 271 0 58 279 0 59 1 21 59 27 0 59 118 1 59 141 29 59 307 0 59 315 0 60 18 30 60 44 19 60 86 21 60 192 1 60 343 0 60 351 0 61 15 24 61 32 24 61 102 26 61 129 27 61 379 0 61 387 0 62 6 14 62 46 1 62 57 12 62 190 17 62 415 0 62 423 0 63 11 29 63 27 1 63 69 10 63 131 25 63 451 0 63 459 0 64 17 1 64 36 28 64 107 31 64 178 9 64 200 0 64 208 0 65 1 15 65 31 4 65 115 12 65 166 29 65 236 0 65 244 0 66 23 16 66 36 14 66 82 9 66 148 20 66 272 0 66 280 0 67 2 21 67 28 0 67 119 1 67 142 29 67 308 0 67 316 0 68 11 15 68 27 1 68 71 7 68 154 8 68 344 0 68 352 0 69 8 25 69 33 24 69 103 26 69 130 27 69 380 0 69 388 0 70 5 15 70 42 18 70 113 7 70 141 30 70 416 0 70 424 0 71 12 29 71 28 1 71 70 10 71 132 25 71 452 0 71 460 0 72 18 1 72 37 28 72 108 31 72 179 9 72 201 0 72 209 0 73 2 15 73 24 5 73 116 12 73 167 29 73 237 0 73 245 0 74 16 17 74 37 14 74 83 9 74 149 20 74 273 0 74 281 0 75 3 21 75 29 0 75 112 2 75 143 29 75 309 0 75 317 0 76 12 15 76 28 1 76 64 8 76 155 8 76 345 0 76 353 0 77 9 25 77 34 24 77 96 27 77 131 27 77 381 0 77 389 0 78 6 15 78 43 18 78 114 7 78 142 30 78 417 0 78 425 0 79 13 29 79 29 1 79 71 10 79 133 25 79 453 0 79 461 0 80 19 1 80 38 28 80 109 31 80 180 9 80 202 0 80 210 0 81 3 15 81 25 5 81 117 12 81 160 30 81 238 0 81 246 0 82 17 17 82 38 14 82 84 9 82 150 20 82 274 0 82 282 0 83 4 21 83 30 0 83 113 2 83 136 30 83 310 0 83 318 0 84 13 15 84 29 1 84 65 8 84 156 8 84 346 0 84 354 0 85 10 25 85 35 24 85 97 27 85 132 27 85 382 0 85 390 0 86 7 15 86 44 18 86 115 7 86 143 30 86 418 0 86 426 0 87 14 29 87 30 1 87 64 11 87 134 25 87 454 0 87 462 0 88 20 1 88 39 28 88 110 31 88 181 9 88 203 0 88 211 0 89 4 15 89 26 5 89 118 12 89 161 30 89 239 0 89 247 0 90 18 17 90 39 14 90 85 9 90 151 20 90 275 0 90 283 0 91 5 21 91 31 0 91 114 2 91 137 30 91 311 0 91 319 0 92 14 15 92 30 1 92 66 8 92 157 8 92 347 0 92 355 0 93 11 25 93 36 24 93 98 27 93 133 27 93 383 0 93 391 0 94 0 16 94 45 18 94 116 7 94 136 31 94 419 0 94 427 0 95 15 29 95 31 1 95 65 11 95 135 25 95 455 0 95 463 0 96 21 1 96 32 29 96 111 31 96 182 9 96 204 0 96 212 0 97 17 11 97 30 7 97 88 14 97 187 30 97 240 0 97 248 0 98 19 17 98 32 15 98 86 9 98 144 21 98 276 0 98 284 0 99 6 0 99 28 30 99 77 26 99 142 2 99 312 0 99 320 0 100 15 15 100 31 1 100 67 8 100 158 8 100 348 0 100 356 0 101 11 19 101 25 11 101 69 4 101 160 6 101 384 0 101 392 0 102 1 16 102 46 18 102 117 7 102 137 31 102 420 0 102 428 0 103 13 2 103 35 5 103 56 17 103 170 9 103 456 0 103 464 0 104 22 1 104 33 29 104 104 0 104 183 9 104 205 0 104 213 0 105 18 11 105 31 7 105 89 14 105 188 30 105 241 0 105 249 0 106 20 17 106 33 15 106 87 9 106 145 21 106 277 0 106 285 0 107 7 0 107 29 30 107 78 26 107 143 2 107 313 0 107 321 0 108 8 16 108 24 2 108 68 8 108 159 8 108 349 0 108 357 0 109 12 19 109 26 11 109 70 4 109 161 6 109 385 0 109 393 0 110 2 16 110 47 18 110 118 7 110 138 31 110 421 0 110 429 0 111 14 2 111 36 5 111 57 17 111 171 9 111 457 0 111 465 0 112 23 1 112 34 29 112 105 0 112 176 10 112 206 0 112 214 0 113 19 11 113 24 8 113 90 14 113 189 30 113 242 0 113 250 0 114 21 17 114 34 15 114 80 10 114 146 21 114 278 0 114 286 0 115 0 1 115 30 30 115 79 26 115 136 3 115 314 0 115 322 0 116 9 16 116 25 2 116 69 8 116 152 9 116 350 0 116 358 0 117 13 19 117 27 11 117 71 4 117 162 6 117 386 0 117 394 0 118 3 16 118 40 19 118 119 7 118 139 31 118 422 0 118 430 0 119 15 2 119 37 5 119 58 17 119 172 9 119 458 0 119 466 0 120 16 2 120 35 29 120 106 0 120 177 10 120 207 0 120 215 0 121 20 11 121 25 8 121 91 14 121 190 30 121 243 0 121 251 0 122 22 17 122 35 15 122 81 10 122 147 21 122 279 0 122 287 0 123 1 1 123 31 30 123 72 27 123 137 3 123 315 0 123 323 0 124 10 16 124 26 2 124 70 8 124 153 9 124 351 0 124 359 0 125 14 19 125 28 11 125 64 5 125 163 6 125 387 0 125 395 0 126 4 16 126 41 19 126 112 8 126 140 31 126 423 0 126 431 0 127 8 3 127 38 5 127 59 17 127 173 9 127 459 0 127 467 0 128 17 21 128 34 25 128 104 13 128 177 7 128 208 0 128 216 0 129 21 11 129 26 8 129 92 14 129 191 30 129 244 0 129 252 0 130 7 1 130 34 15 130 84 0 130 145 23 130 280 0 130 288 0 131 2 1 131 24 31 131 73 27 131 138 3 131 316 0 131 324 0 132 15 8 132 47 23 132 95 19 132 156 14 132 352 0 132 360 0 133 15 19 133 29 11 133 65 5 133 164 6 133 388 0 133 396 0 134 15 13 134 26 31 134 63 15 134 151 10 134 424 0 134 432 0 135 9 3 135 39 5 135 60 17 135 174 9 135 460 0 135 468 0 136 18 21 136 35 25 136 105 13 136 178 7 136 209 0 136 217 0 137 22 11 137 27 8 137 93 14 137 184 31 137 245 0 137 253 0 138 0 2 138 35 15 138 85 0 138 146 23 138 281 0 138 289 0 139 3 1 139 25 31 139 74 27 139 139 3 139 317 0 139 325 0 140 8 9 140 40 24 140 88 20 140 157 14 140 353 0 140 361 0 141 8 20 141 30 11 141 66 5 141 165 6 141 389 0 141 397 0 142 8 14 142 27 31 142 56 16 142 144 11 142 425 0 142 433 0 143 10 3 143 32 6 143 61 17 143 175 9 143 461 0 143 469 0 144 19 21 144 36 25 144 106 13 144 179 7 144 210 0 144 218 0 145 23 11 145 28 8 145 94 14 145 185 31 145 246 0 145 254 0 146 1 2 146 36 15 146 86 0 146 147 23 146 282 0 146 290 0 147 4 1 147 26 31 147 75 27 147 140 3 147 318 0 147 326 0 148 9 9 148 41 24 148 89 20 148 158 14 148 354 0 148 362 0 149 9 20 149 31 11 149 67 5 149 166 6 149 390 0 149 398 0 150 9 14 150 28 31 150 57 16 150 145 11 150 426 0 150 434 0 151 11 3 151 33 6 151 62 17 151 168 10 151 462 0 151 470 0 152 20 21 152 37 25 152 107 13 152 180 7 152 211 0 152 219 0 153 16 12 153 29 8 153 95 14 153 186 31 153 247 0 153 255 0 154 2 2 154 37 15 154 87 0 154 148 23 154 283 0 154 291 0 155 5 1 155 27 31 155 76 27 155 141 3 155 319 0 155 327 0 156 10 9 156 42 24 156 90 20 156 159 14 156 355 0 156 363 0 157 10 20 157 24 12 157 68 5 157 167 6 157 391 0 157 399 0 158 10 14 158 29 31 158 58 16 158 146 11 158 427 0 158 435 0 159 12 3 159 34 6 159 63 17 159 169 10 159 463 0 159 471 0 160 21 21 160 38 25 160 108 13 160 181 7 160 212 0 160 220 0 161 10 26 161 36 3 161 97 17 161 158 15 161 248 0 161 256 0 162 3 2 162 38 15 162 80 1 162 149 23 162 284 0 162 292 0 163 2 28 163 35 23 163 78 2 163 152 30 163 320 0 163 328 0 164 11 9 164 43 24 164 91 20 164 152 15 164 356 0 164 364 0 165 5 24 165 22 15 165 45 2 165 54 29 165 165 8 165 392 0 165 400 0 166 11 14 166 30 31 166 59 16 166 147 11 166 428 0 166 436 0 167 26 29 167 95 19 167 128 13 167 464 0 167 472 0 168 22 21 168 39 25 168 109 13 168 182 7 168 213 0 168 221 0 169 11 26 169 37 3 169 98 17 169 159 15 169 249 0 169 257 0 170 4 2 170 39 15 170 81 1 170 150 23 170 285 0 170 293 0 171 3 28 171 36 23 171 79 2 171 153 30 171 321 0 171 329 0 172 12 9 172 44 24 172 92 20 172 153 15 172 357 0 172 365 0 173 6 24 173 23 15 173 46 2 173 55 29 173 166 8 173 393 0 173 401 0 174 12 14 174 31 31 174 60 16 174 148 11 174 429 0 174 437 0 175 27 29 175 88 20 175 129 13 175 465 0 175 473 0 176 23 21 176 32 26 176 110 13 176 183 7 176 214 0 176 222 0 177 12 26 177 38 3 177 99 17 177 152 16 177 250 0 177 258 0 178 5 2 178 32 16 178 82 1 178 151 23 178 286 0 178 294 0 179 4 28 179 37 23 179 72 3 179 154 30 179 322 0 179 330 0 180 13 9 180 45 24 180 93 20 180 154 15 180 358 0 180 366 0 181 7 24 181 16 16 181 47 2 181 48 30 181 167 8 181 394 0 181 402 0 182 13 14 182 24 0 182 61 16 182 149 11 182 430 0 182 438 0 183 28 29 183 89 20 183 130 13 183 466 0 183 474 0 184 16 22 184 33 26 184 111 13 184 176 8 184 215 0 184 223 0 185 13 26 185 39 3 185 100 17 185 153 16 185 251 0 185 259 0 186 6 2 186 33 16 186 83 1 186 144 24 186 287 0 186 295 0 187 5 28 187 38 23 187 73 3 187 155 30 187 323 0 187 331 0 188 14 9 188 46 24 188 94 20 188 155 15 188 359 0 188 367 0 189 0 25 189 17 16 189 40 3 189 49 30 189 160 9 189 395 0 189 403 0 190 14 14 190 25 0 190 62 16 190 150 11 190 431 0 190 439 0 191 29 29 191 90 20 191 131 13 191 467 0 191 475 0 192 1 20 192 19 18 192 39 12 192 122 1 192 171 28 192 216 0 192 224 0 193 14 26 193 32 4 193 101 17 193 154 16 193 252 0 193 260 0 194 36 9 194 110 19 194 183 11 194 288 0 194 296 0 195 6 28 195 39 23 195 74 3 195 156 30 195 324 0 195 332 0 196 0 31 196 46 5 196 72 5 196 141 10 196 360 0 196 368 0 197 1 25 197 18 16 197 41 3 197 50 30 197 161 9 197 396 0 197 404 0 198 21 10 198 40 29 198 50 5 198 125 2 198 432 0 198 440 0 199 30 29 199 91 20 199 132 13 199 468 0 199 476 0 200 2 20 200 20 18 200 32 13 200 123 1 200 172 28 200 217 0 200 225 0 201 15 26 201 33 4 201 102 17 201 155 16 201 253 0 201 261 0 202 37 9 202 111 19 202 176 12 202 289 0 202 297 0 203 7 28 203 32 24 203 75 3 203 157 30 203 325 0 203 333 0 204 1 31 204 47 5 204 73 5 204 142 10 204 361 0 204 369 0 205 2 25 205 19 16 205 42 3 205 51 30 205 162 9 205 397 0 205 405 0 206 22 10 206 41 29 206 51 5 206 126 2 206 433 0 206 441 0 207 31 29 207 92 20 207 133 13 207 469 0 207 477 0 208 3 20 208 21 18 208 33 13 208 124 1 208 173 28 208 218 0 208 226 0 209 8 27 209 34 4 209 103 17 209 156 16 209 254 0 209 262 0 210 38 9 210 104 20 210 177 12 210 290 0 210 298 0 211 0 29 211 33 24 211 76 3 211 158 30 211 326 0 211 334 0 212 2 31 212 40 6 212 74 5 212 143 10 212 362 0 212 370 0 213 3 25 213 20 16 213 43 3 213 52 30 213 163 9 213 398 0 213 406 0 214 23 10 214 42 29 214 52 5 214 127 2 214 434 0 214 442 0 215 24 30 215 93 20 215 134 13 215 470 0 215 478 0 216 4 20 216 22 18 216 34 13 216 125 1 216 174 28 216 219 0 216 227 0 217 9 27 217 35 4 217 96 18 217 157 16 217 255 0 217 263 0 218 39 9 218 105 20 218 178 12 218 291 0 218 299 0 219 1 29 219 34 24 219 77 3 219 159 30 219 327 0 219 335 0 220 3 31 220 41 6 220 75 5 220 136 11 220 363 0 220 371 0 221 4 25 221 21 16 221 44 3 221 53 30 221 164 9 221 399 0 221 407 0 222 16 11 222 43 29 222 53 5 222 120 3 222 435 0 222 443 0 223 25 30 223 94 20 223 135 13 223 471 0 223 479 0 224 5 20 224 23 18 224 35 13 224 126 1 224 175 28 224 220 0 224 228 0 225 26 22 225 45 23 225 85 1 225 167 18 225 256 0 225 264 0 226 32 10 226 106 20 226 179 12 226 292 0 226 300 0 227 15 1 227 24 11 227 64 30 227 128 12 227 328 0 227 336 0 228 4 31 228 42 6 228 76 5 228 137 11 228 364 0 228 372 0 229 0 20 229 41 3 229 94 10 229 122 20 229 400 0 229 408 0 230 17 11 230 44 29 230 54 5 230 121 3 230 436 0 230 444 0 231 7 7 231 23 23 231 44 19 231 51 17 231 127 1 231 194 0 231 472 0 232 6 20 232 16 19 232 36 13 232 127 1 232 168 29 232 221 0 232 229 0 233 27 22 233 46 23 233 86 1 233 160 19 233 257 0 233 265 0 234 33 10 234 107 20 234 180 12 234 293 0 234 301 0 235 8 2 235 25 11 235 65 30 235 129 12 235 329 0 235 337 0 236 5 31 236 43 6 236 77 5 236 138 11 236 365 0 236 373 0 237 1 20 237 42 3 237 95 10 237 123 20 237 401 0 237 409 0 238 18 11 238 45 29 238 55 5 238 122 3 238 437 0 238 445 0 239 0 8 239 16 24 239 45 19 239 52 17 239 120 2 239 195 0 239 473 0 240 7 20 240 17 19 240 37 13 240 120 2 240 169 29 240 222 0 240 230 0 241 28 22 241 47 23 241 87 1 241 161 19 241 258 0 241 266 0 242 34 10 242 108 20 242 181 12 242 294 0 242 302 0 243 9 2 243 26 11 243 66 30 243 130 12 243 330 0 243 338 0 244 6 31 244 44 6 244 78 5 244 139 11 244 366 0 244 374 0 245 2 20 245 43 3 245 88 11 245 124 20 245 402 0 245 410 0 246 19 11 246 46 29 246 48 6 246 123 3 246 438 0 246 446 0 247 1 8 247 17 24 247 46 19 247 53 17 247 121 2 247 196 0 247 474 0 248 0 21 248 18 19 248 38 13 248 121 2 248 170 29 248 223 0 248 231 0 249 29 22 249 40 24 249 80 2 249 162 19 249 259 0 249 267 0 250 35 10 250 109 20 250 182 12 250 295 0 250 303 0 251 10 2 251 27 11 251 67 30 251 131 12 251 331 0 251 339 0 252 7 31 252 45 6 252 79 5 252 140 11 252 367 0 252 375 0 253 3 20 253 44 3 253 89 11 253 125 20 253 403 0 253 411 0 254 20 11 254 47 29 254 49 6 254 124 3 254 439 0 254 447 0 255 2 8 255 18 24 255 47 19 255 54 17 255 122 2 255 197 0 255 475 0 256 8 23 256 33 20 256 101 28 256 171 13 256 224 0 256 232 0 257 30 22 257 41 24 257 81 2 257 163 19 257 260 0 257 268 0 258 8 11 258 44 2 258 76 27 258 178 8 258 296 0 258 304 0 259 11 2 259 28 11 259 68 30 259 132 12 259 332 0 259 340 0 260 23 15 260 24 26 260 57 11 260 190 13 260 368 0 260 376 0 261 4 20 261 45 3 261 90 11 261 126 20 261 404 0 261 412 0 262 18 20 262 48 27 262 104 23 262 174 23 262 440 0 262 448 0 263 3 8 263 19 24 263 40 20 263 55 17 263 123 2 263 198 0 263 476 0 264 9 23 264 34 20 264 102 28 264 172 13 264 225 0 264 233 0 265 31 22 265 42 24 265 82 2 265 164 19 265 261 0 265 269 0 266 9 11 266 45 2 266 77 27 266 179 8 266 297 0 266 305 0 267 12 2 267 29 11 267 69 30 267 133 12 267 333 0 267 341 0 268 16 16 268 25 26 268 58 11 268 191 13 268 369 0 268 377 0 269 5 20 269 46 3 269 91 11 269 127 20 269 405 0 269 413 0 270 19 20 270 49 27 270 105 23 270 175 23 270 441 0 270 449 0 271 4 8 271 20 24 271 41 20 271 48 18 271 124 2 271 199 0 271 477 0 272 10 23 272 35 20 272 103 28 272 173 13 272 226 0 272 234 0 273 24 23 273 43 24 273 83 2 273 165 19 273 262 0 273 270 0 274 10 11 274 46 2 274 78 27 274 180 8 274 298 0 274 306 0 275 13 2 275 30 11 275 70 30 275 134 12 275 334 0 275 342 0 276 17 16 276 26 26 276 59 11 276 184 14 276 370 0 276 378 0 277 6 20 277 47 3 277 92 11 277 120 21 277 406 0 277 414 0 278 20 20 278 50 27 278 106 23 278 168 24 278 442 0 278 450 0 279 5 8 279 21 24 279 42 20 279 49 18 279 125 2 279 192 1 279 478 0 280 11 23 280 36 20 280 96 29 280 174 13 280 227 0 280 235 0 281 25 23 281 44 24 281 84 2 281 166 19 281 263 0 281 271 0 282 11 11 282 47 2 282 79 27 282 181 8 282 299 0 282 307 0 283 14 2 283 31 11 283 71 30 283 135 12 283 335 0 283 343 0 284 18 16 284 27 26 284 60 11 284 185 14 284 371 0 284 379 0 285 7 20 285 40 4 285 93 11 285 121 21 285 407 0 285 415 0 286 21 20 286 51 27 286 107 23 286 169 24 286 443 0 286 451 0 287 6 8 287 22 24 287 43 20 287 50 18 287 126 2 287 193 1 287 479 0

APPENDIX TABLE C Specification of the base matrix B_(1/2) for the rate-½ LDPC code 0 6 16 0 24 12 0 42 16 0 101 9 0 153 21 0 234 3 0 240 0 0 248 0 1 15 24 1 21 1 1 42 30 1 93 17 1 155 15 1 228 29 1 270 0 1 278 0 2 20 3 2 54 19 2 73 23 2 146 2 2 211 18 2 300 0 2 308 0 3 28 23 3 44 13 3 84 3 3 153 11 3 205 0 3 330 0 3 338 0 4 4 29 4 14 22 4 45 25 4 77 28 4 129 9 4 241 0 4 360 0 4 368 0 5 4 13 5 25 22 5 32 8 5 56 30 5 146 9 5 238 8 5 390 0 5 398 0 6 0 4 6 10 6 6 35 29 6 54 7 6 166 23 6 219 0 6 420 0 6 428 0 7 16 0 7 26 29 7 52 1 7 107 11 7 171 5 7 450 0 7 458 0 8 7 16 8 25 12 8 43 16 8 102 9 8 154 21 8 235 3 8 241 0 8 249 0 9 8 25 9 22 1 9 43 30 9 94 17 9 156 15 9 229 29 9 271 0 9 279 0 10 21 3 10 55 19 10 74 23 10 147 2 10 212 18 10 301 0 10 309 0 11 29 23 11 45 13 11 85 3 11 154 11 11 206 0 11 331 0 11 339 0 12 5 29 12 15 22 12 46 25 12 78 28 12 130 9 12 242 0 12 361 0 12 369 0 13 5 13 13 26 22 13 33 8 13 57 30 13 147 9 13 239 8 13 391 0 13 399 0 14 1 4 14 11 6 14 36 29 14 55 7 14 167 23 14 220 0 14 421 0 14 429 0 15 17 0 15 27 29 15 53 1 15 108 11 15 172 5 15 451 0 15 459 0 16 0 17 16 26 12 16 44 16 16 103 9 16 155 21 16 236 3 16 242 0 16 250 0 17 15 18 17 28 26 17 32 25 17 85 24 17 136 0 17 208 0 17 272 0 17 280 0 18 22 3 18 48 20 18 75 23 18 148 2 18 213 18 18 302 0 18 310 0 19 30 23 19 46 13 19 86 3 19 155 11 19 207 0 19 332 0 19 340 0 20 6 29 20 8 23 20 47 25 20 79 28 20 131 9 20 243 0 20 362 0 20 370 0 21 14 1 21 50 7 21 59 1 21 145 2 21 187 27 21 392 0 21 400 0 22 2 4 22 12 6 22 37 29 22 48 8 22 160 24 22 221 0 22 422 0 22 430 0 23 18 0 23 28 29 23 54 1 23 109 11 23 173 5 23 452 0 23 460 0 24 1 17 24 27 12 24 45 16 24 96 10 24 156 21 24 237 3 24 243 0 24 251 0 25 8 19 25 29 26 25 33 25 25 86 24 25 137 0 25 209 0 25 273 0 25 281 0 26 23 3 26 49 20 26 76 23 26 149 2 26 214 18 26 303 0 26 311 0 27 31 23 27 47 13 27 87 3 27 156 11 27 200 1 27 333 0 27 341 0 28 7 29 28 9 23 28 40 26 28 72 29 28 132 9 28 244 0 28 363 0 28 371 0 29 15 1 29 51 7 29 60 1 29 146 2 29 188 27 29 393 0 29 401 0 30 3 4 30 13 6 30 38 29 30 49 8 30 161 24 30 222 0 30 423 0 30 431 0 31 19 0 31 29 29 31 55 1 31 110 11 31 174 5 31 453 0 31 461 0 32 2 17 32 28 12 32 46 16 32 97 10 32 157 21 32 238 3 32 244 0 32 252 0 33 9 19 33 30 26 33 34 25 33 87 24 33 138 0 33 210 0 33 274 0 33 282 0 34 17 29 34 52 6 34 68 8 34 152 9 34 193 0 34 304 0 34 312 0 35 24 24 35 40 14 35 80 4 35 157 11 35 201 1 35 334 0 35 342 0 36 0 30 36 10 23 36 41 26 36 73 29 36 133 9 36 245 0 36 364 0 36 372 0 37 8 2 37 52 7 37 61 1 37 147 2 37 189 27 37 394 0 37 402 0 38 0 11 38 8 6 38 54 21 38 97 23 38 121 16 38 168 6 38 424 0 38 432 0 39 20 0 39 30 29 39 48 2 39 111 11 39 175 5 39 454 0 39 462 0 40 3 17 40 29 12 40 47 16 40 98 10 40 158 21 40 239 3 40 245 0 40 253 0 41 10 19 41 31 26 41 35 25 41 80 25 41 139 0 41 211 0 41 275 0 41 283 0 42 18 29 42 53 6 42 69 8 42 153 9 42 194 0 42 305 0 42 313 0 43 25 24 43 41 14 43 81 4 43 158 11 43 202 1 43 335 0 43 343 0 44 1 30 44 11 23 44 42 26 44 74 29 44 134 9 44 246 0 44 365 0 44 373 0 45 9 2 45 53 7 45 62 1 45 148 2 45 190 27 45 395 0 45 403 0 46 1 11 46 9 6 46 55 21 46 98 23 46 122 16 46 169 6 46 425 0 46 433 0 47 21 0 47 31 29 47 49 2 47 104 12 47 168 6 47 455 0 47 463 0 48 4 17 48 30 12 48 40 17 48 99 10 48 159 21 48 232 4 48 246 0 48 254 0 49 11 19 49 24 27 49 36 25 49 81 25 49 140 0 49 212 0 49 276 0 49 284 0 50 19 29 50 54 6 50 70 8 50 154 9 50 195 0 50 306 0 50 314 0 51 20 24 51 29 25 51 55 16 51 58 17 51 123 16 51 186 16 51 336 0 51 344 0 52 2 30 52 12 23 52 43 26 52 75 29 52 135 9 52 247 0 52 366 0 52 374 0 53 10 2 53 54 7 53 63 1 53 149 2 53 191 27 53 396 0 53 404 0 54 2 11 54 10 6 54 48 22 54 99 23 54 123 16 54 170 6 54 426 0 54 434 0 55 21 9 55 37 14 55 105 16 55 138 31 55 183 18 55 456 0 55 464 0 56 5 17 56 31 12 56 41 17 56 100 10 56 152 22 56 233 4 56 247 0 56 255 0 57 12 19 57 25 27 57 37 25 57 82 25 57 141 0 57 213 0 57 277 0 57 285 0 58 20 29 58 55 6 58 71 8 58 155 9 58 196 0 58 307 0 58 315 0 59 21 24 59 30 25 59 48 17 59 59 17 59 124 16 59 187 16 59 337 0 59 345 0 60 3 30 60 13 23 60 44 26 60 76 29 60 128 10 60 240 1 60 367 0 60 375 0 61 11 2 61 55 7 61 56 2 61 150 2 61 184 28 61 397 0 61 405 0 62 3 11 62 11 6 62 49 22 62 100 23 62 124 16 62 171 6 62 427 0 62 435 0 63 22 9 63 38 14 63 106 16 63 139 31 63 176 19 63 457 0 63 465 0 64 5 0 64 22 16 64 40 23 64 99 15 64 147 18 64 230 15 64 248 0 64 256 0 65 13 19 65 26 27 65 38 25 65 83 25 65 142 0 65 214 0 65 278 0 65 286 0 66 21 29 66 48 7 66 64 9 66 156 9 66 197 0 66 308 0 66 316 0 67 22 24 67 31 25 67 49 17 67 60 17 67 125 16 67 188 16 67 338 0 67 346 0 68 3 20 68 24 6 68 45 11 68 68 3 68 135 18 68 197 4 68 368 0 68 376 0 69 12 2 69 48 8 69 57 2 69 151 2 69 185 28 69 398 0 69 406 0 70 4 11 70 12 6 70 50 22 70 101 23 70 125 16 70 172 6 70 428 0 70 436 0 71 23 9 71 39 14 71 107 16 71 140 31 71 177 19 71 458 0 71 466 0 72 6 0 72 23 16 72 41 23 72 100 15 72 148 18 72 231 15 72 249 0 72 257 0 73 14 19 73 27 27 73 39 25 73 84 25 73 143 0 73 215 0 73 279 0 73 287 0 74 22 29 74 49 7 74 65 9 74 157 9 74 198 0 74 309 0 74 317 0 75 23 24 75 24 26 75 50 17 75 61 17 75 126 16 75 189 16 75 339 0 75 347 0 76 4 20 76 25 6 76 46 11 76 69 3 76 128 19 76 198 4 76 369 0 76 377 0 77 13 2 77 49 8 77 58 2 77 144 3 77 186 28 77 399 0 77 407 0 78 5 11 78 13 6 78 51 22 78 102 23 78 126 16 78 173 6 78 429 0 78 437 0 79 16 10 79 32 15 79 108 16 79 141 31 79 178 19 79 459 0 79 467 0 80 7 0 80 16 17 80 42 23 80 101 15 80 149 18 80 224 16 80 250 0 80 258 0 81 5 0 81 27 0 81 44 31 81 91 31 81 131 10 81 237 24 81 280 0 81 288 0 82 23 29 82 50 7 82 66 9 82 158 9 82 199 0 82 310 0 82 318 0 83 16 25 83 25 26 83 51 17 83 62 17 83 127 16 83 190 16 83 340 0 83 348 0 84 5 20 84 26 6 84 47 11 84 70 3 84 129 19 84 199 4 84 370 0 84 378 0 85 14 12 85 25 20 85 54 9 85 101 30 85 126 7 85 191 14 85 400 0 85 408 0 86 6 11 86 14 6 86 52 22 86 103 23 86 127 16 86 174 6 86 430 0 86 438 0 87 17 10 87 33 15 87 109 16 87 142 31 87 179 19 87 460 0 87 468 0 88 0 1 88 17 17 88 43 23 88 102 15 88 150 18 88 225 16 88 251 0 88 259 0 89 6 0 89 28 0 89 45 31 89 92 31 89 132 10 89 238 24 89 281 0 89 289 0 90 16 30 90 51 7 90 67 9 90 159 9 90 192 1 90 311 0 90 319 0 91 17 25 91 26 26 91 52 17 91 63 17 91 120 17 91 191 16 91 341 0 91 349 0 92 6 20 92 27 6 92 40 12 92 71 3 92 130 19 92 192 5 92 371 0 92 379 0 93 15 12 93 26 20 93 55 9 93 102 30 93 127 7 93 184 15 93 401 0 93 409 0 94 7 11 94 15 6 94 53 22 94 96 24 94 120 17 94 175 6 94 431 0 94 439 0 95 18 10 95 34 15 95 110 16 95 143 31 95 180 19 95 461 0 95 469 0 96 1 1 96 18 17 96 44 23 96 103 15 96 151 18 96 226 16 96 252 0 96 260 0 97 7 0 97 29 0 97 46 31 97 93 31 97 133 10 97 239 24 97 282 0 97 290 0 98 16 2 98 44 11 98 91 8 98 129 5 98 196 9 98 312 0 98 320 0 99 18 25 99 27 26 99 53 17 99 56 18 99 121 17 99 184 17 99 342 0 99 350 0 100 7 20 100 28 6 100 41 12 100 64 4 100 131 19 100 193 5 100 372 0 100 380 0 101 8 13 101 27 20 101 48 10 101 103 30 101 120 8 101 185 15 101 402 0 101 410 0 102 7 9 102 19 25 102 50 11 102 75 27 102 160 28 102 220 29 102 432 0 102 440 0 103 19 10 103 35 15 103 111 16 103 136 0 103 181 19 103 462 0 103 470 0 104 2 1 104 19 17 104 45 23 104 96 16 104 144 19 104 227 16 104 253 0 104 261 0 105 0 1 105 30 0 105 47 31 105 94 31 105 134 10 105 232 25 105 283 0 105 291 0 106 17 2 106 45 11 106 92 8 106 130 5 106 197 9 106 313 0 106 321 0 107 19 25 107 28 26 107 54 17 107 57 18 107 122 17 107 185 17 107 343 0 107 351 0 108 0 21 108 29 6 108 42 12 108 65 4 108 132 19 108 194 5 108 373 0 108 381 0 109 9 13 109 28 20 109 49 10 109 96 31 109 121 8 109 186 15 109 403 0 109 411 0 110 0 10 110 20 25 110 51 11 110 76 27 110 161 28 110 221 29 110 433 0 110 441 0 111 20 10 111 36 15 111 104 17 111 137 0 111 182 19 111 463 0 111 471 0 112 3 1 112 20 17 112 46 23 112 97 16 112 145 19 112 228 16 112 254 0 112 262 0 113 1 1 113 31 0 113 40 0 113 95 31 113 135 10 113 233 25 113 284 0 113 292 0 114 18 2 114 46 11 114 93 8 114 131 5 114 198 9 114 314 0 114 322 0 115 19 14 115 24 11 115 34 31 115 84 18 115 137 12 115 206 4 115 344 0 115 352 0 116 1 21 116 30 6 116 43 12 116 66 4 116 133 19 116 195 5 116 374 0 116 382 0 117 10 13 117 29 20 117 50 10 117 97 31 117 122 8 117 187 15 117 404 0 117 412 0 118 1 10 118 21 25 118 52 11 118 77 27 118 162 28 118 222 29 118 434 0 118 442 0 119 8 20 119 38 17 119 45 24 119 72 22 119 117 0 119 181 7 119 464 0 119 472 0 120 4 1 120 21 17 120 47 23 120 98 16 120 146 19 120 229 16 120 255 0 120 263 0 121 2 1 121 24 1 121 41 0 121 88 0 121 128 11 121 234 25 121 285 0 121 293 0 122 19 2 122 47 11 122 94 8 122 132 5 122 199 9 122 315 0 122 323 0 123 20 14 123 25 11 123 35 31 123 85 18 123 138 12 123 207 4 123 345 0 123 353 0 124 2 21 124 31 6 124 44 12 124 67 4 124 134 19 124 196 5 124 375 0 124 383 0 125 11 13 125 30 20 125 51 10 125 98 31 125 123 8 125 188 15 125 405 0 125 413 0 126 2 10 126 22 25 126 53 11 126 78 27 126 163 28 126 223 29 126 435 0 126 443 0 127 9 20 127 39 17 127 46 24 127 73 22 127 118 0 127 182 7 127 465 0 127 473 0 128 2 22 128 32 0 128 45 8 128 93 27 128 162 18 128 221 27 128 256 0 128 264 0 129 3 1 129 25 1 129 42 0 129 89 0 129 129 11 129 235 25 129 286 0 129 294 0 130 20 2 130 40 12 130 95 8 130 133 5 130 192 10 130 316 0 130 324 0 131 21 14 131 26 11 131 36 31 131 86 18 131 139 12 131 200 5 131 346 0 131 354 0 132 0 31 132 10 7 132 38 7 132 70 21 132 106 23 132 168 29 132 376 0 132 384 0 133 12 13 133 31 20 133 52 10 133 99 31 133 124 8 133 189 15 133 406 0 133 414 0 134 3 10 134 23 25 134 54 11 134 79 27 134 164 28 134 216 30 134 436 0 134 444 0 135 10 20 135 32 18 135 47 24 135 74 22 135 119 0 135 183 7 135 466 0 135 474 0 136 3 22 136 33 0 136 46 8 136 94 27 136 163 18 136 222 27 136 257 0 136 265 0 137 4 1 137 26 1 137 43 0 137 90 0 137 130 11 137 236 25 137 287 0 137 295 0 138 21 2 138 41 12 138 88 9 138 134 5 138 193 10 138 317 0 138 325 0 139 22 14 139 27 11 139 37 31 139 87 18 139 140 12 139 201 5 139 347 0 139 355 0 140 1 31 140 11 7 140 39 7 140 71 21 140 107 23 140 169 29 140 377 0 140 385 0 141 13 13 141 24 21 141 53 10 141 100 31 141 125 8 141 190 15 141 407 0 141 415 0 142 4 10 142 16 26 142 55 11 142 72 28 142 165 28 142 217 30 142 437 0 142 445 0 143 11 20 143 33 18 143 40 25 143 75 22 143 112 1 143 176 8 143 467 0 143 475 0 144 4 22 144 34 0 144 47 8 144 95 27 144 164 18 144 223 27 144 258 0 144 266 0 145 26 6 145 35 5 145 84 7 145 121 9 145 206 14 145 288 0 145 296 0 146 22 2 146 42 12 146 89 9 146 135 5 146 194 10 146 318 0 146 326 0 147 23 14 147 28 11 147 38 31 147 80 19 147 141 12 147 202 5 147 348 0 147 356 0 148 2 31 148 12 7 148 32 8 148 64 22 148 108 23 148 170 29 148 378 0 148 386 0 149 13 20 149 32 11 149 55 27 149 139 12 149 170 15 149 408 0 149 416 0 150 5 10 150 17 26 150 48 12 150 73 28 150 166 28 150 218 30 150 438 0 150 446 0 151 12 20 151 34 18 151 41 25 151 76 22 15 113 1 151 177 8 151 468 0 151 476 0 152 5 22 152 35 0 152 40 9 152 88 28 152 165 18 152 216 28 152 259 0 152 267 0 153 27 6 153 36 5 153 85 7 153 122 9 153 207 14 153 289 0 153 297 0 154 23 2 154 43 12 154 90 9 154 128 6 154 195 10 154 319 0 154 327 0 155 16 15 155 29 11 155 39 31 155 81 19 155 142 12 155 203 5 155 349 0 155 357 0 156 3 31 156 13 7 156 33 8 156 65 22 156 109 23 156 171 29 156 379 0 156 387 0 157 14 20 157 33 11 157 48 28 157 140 12 157 171 15 157 409 0 157 417 0 158 6 10 158 18 26 158 49 12 158 74 28 158 167 28 158 219 30 158 439 0 158 447 0 159 13 20 159 35 18 159 42 25 159 77 22 159 114 1 159 178 8 159 469 0 159 477 0 160 6 22 160 36 0 160 41 9 160 89 28 160 166 18 160 217 28 160 260 0 160 268 0 161 28 6 161 37 5 161 86 7 161 123 9 161 200 15 161 290 0 161 298 0 162 9 13 162 26 25 162 44 9 162 68 25 162 119 14 162 228 2 162 320 0 162 328 0 163 17 15 163 30 11 163 32 0 163 82 19 163 143 12 163 204 5 163 350 0 163 358 0 164 4 31 164 14 7 164 34 8 164 66 22 164 110 23 164 172 29 164 380 0 164 388 0 165 15 20 165 34 11 165 49 28 165 141 12 165 172 15 165 410 0 165 418 0 166 23 5 166 37 10 166 53 31 166 116 5 166 209 25 166 440 0 166 448 0 167 14 20 167 36 18 167 43 25 167 78 22 167 115 1 167 179 8 167 470 0 167 478 0 168 7 22 168 37 0 168 42 9 168 90 28 168 167 18 168 218 28 168 261 0 168 269 0 169 29 6 169 38 5 169 87 7 169 124 9 169 201 15 169 291 0 169 299 0 170 10 13 170 27 25 170 45 9 170 69 25 170 112 15 170 229 2 170 321 0 170 329 0 171 18 15 171 31 11 171 33 0 171 83 19 171 136 13 171 205 5 171 351 0 171 359 0 172 5 31 172 15 7 172 35 8 172 67 22 172 111 23 172 173 29 172 381 0 172 389 0 173 8 21 173 35 11 173 50 28 173 142 12 173 173 15 173 411 0 173 419 0 174 16 6 174 38 10 174 54 31 174 117 5 174 210 25 174 441 0 174 449 0 175 15 20 175 37 18 175 44 25 175 79 22 175 116 1 175 180 8 175 471 0 175 479 0 176 0 23 176 38 0 176 43 9 176 91 28 176 160 19 176 219 28 176 262 0 176 270 0 177 30 6 177 39 5 177 80 8 177 125 9 177 202 15 177 292 0 177 300 0 178 11 13 178 28 25 178 46 9 178 70 25 178 113 15 178 230 2 178 322 0 178 330 0 179 6 26 179 22 0 179 41 25 179 60 4 179 105 21 179 176 31 179 352 0 179 360 0 180 6 31 180 8 8 180 36 8 180 68 22 180 104 24 180 174 29 180 382 0 180 390 0 181 9 21 181 36 11 181 51 28 181 143 12 181 174 15 181 412 0 181 420 0 182 17 6 182 39 10 182 55 31 182 118 5 182 211 25 182 442 0 182 450 0 183 9 15 183 37 19 183 48 3 183 118 12 183 165 12 183 242 0 183 472 0 184 1 23 184 39 0 184 44 9 184 92 28 184 161 19 184 220 28 184 263 0 184 271 0 185 31 6 185 32 6 185 81 8 185 126 9 185 203 15 185 293 0 185 301 0 186 12 13 186 29 25 186 47 9 186 73 25 186 114 15 186 231 2 186 323 0 186 331 0 187 7 26 187 23 0 187 42 25 187 61 4 187 106 21 187 177 31 187 353 0 187 361 0 188 7 31 188 9 8 188 37 8 188 69 22 188 105 24 188 175 29 188 383 0 188 391 0 189 10 21 189 37 11 189 52 28 189 136 13 189 175 15 189 413 0 189 421 0 190 18 6 190 32 11 190 48 0 190 119 5 190 212 25 190 443 0 190 451 0 191 10 15 191 38 19 191 49 3 191 119 12 191 166 12 191 243 0 191 473 0 192 9 24 192 23 0 192 44 29 192 95 16 192 157 14 192 230 28 192 264 0 192 272 0 193 24 7 193 33 6 193 82 8 193 127 9 193 204 15 193 294 0 193 302 0 194 13 13 194 30 25 194 40 10 194 64 26 194 115 15 194 224 3 194 324 0 194 332 0 195 0 27 195 16 1 195 43 25 195 62 4 195 107 21 195 178 31 195 354 0 195 362 0 196 6 12 196 27 21 196 34 7 196 58 29 196 148 8 196 232 8 196 384 0 196 392 0 197 11 21 197 38 11 197 53 28 197 137 13 197 168 16 197 414 0 197 422 0 198 19 6 198 33 11 198 49 0 198 112 6 198 213 25 198 444 0 198 452 0 199 11 15 199 39 19 199 50 3 199 112 13 199 167 12 199 244 0 199 474 0 200 10 24 200 16 1 200 45 29 200 88 17 200 158 14 200 231 28 200 265 0 200 273 0 201 25 7 201 34 6 201 83 8 201 120 10 201 205 15 201 295 0 201 303 0 202 14 13 202 31 25 202 41 10 202 65 26 202 116 15 202 225 3 202 325 0 202 333 0 203 1 27 203 17 1 203 44 25 203 63 4 203 108 21 203 179 31 203 355 0 203 363 0 204 7 12 204 28 21 204 35 7 204 59 29 204 149 8 204 233 8 204 385 0 204 393 0 205 12 21 205 39 11 205 54 28 205 138 13 205 169 16 205 415 0 205 423 0 206 20 6 206 34 11 206 50 0 206 113 6 206 214 25 206 445 0 206 453 0 207 12 15 207 32 20 207 51 3 207 113 13 207 160 13 207 245 0 207 475 0 208 11 24 208 17 1 208 46 29 208 89 17 208 159 14 208 224 29 208 266 0 208 274 0 209 16 3 209 50 19 209 77 22 209 150 1 209 215 17 209 296 0 209 304 0 210 15 13 210 24 26 210 42 10 210 66 26 210 117 15 210 226 3 210 326 0 210 334 0 211 2 27 211 18 1 211 45 25 211 56 5 211 109 21 211 180 31 211 356 0 211 364 0 212 0 13 212 29 21 212 36 7 212 60 29 212 150 8 212 234 8 212 386 0 212 394 0 213 4 3 213 14 5 213 39 28 213 50 7 213 162 23 213 223 31 213 416 0 213 424 0 214 21 6 214 35 11 214 51 0 214 114 6 214 215 25 214 446 0 214 454 0 215 13 15 215 33 20 215 52 3 215 114 13 215 161 13 215 246 0 215 476 0 216 12 24 216 18 1 216 47 29 216 90 17 216 152 15 216 225 29 216 267 0 216 275 0 217 17 3 217 51 19 217 78 22 217 151 1 217 208 18 217 297 0 217 305 0 218 8 14 218 25 26 218 43 10 218 67 26 218 118 15 218 227 3 218 327 0 218 335 0 219 3 27 219 19 1 219 46 25 219 57 5 219 110 21 219 181 31 219 357 0 219 365 0 220 1 13 220 30 21 220 37 7 220 61 29 220 151 8 220 235 8 220 387 0 220 395 0 221 5 3 221 15 5 221 32 29 221 51 7 221 163 23 221 216 0 221 417 0 221 425 0 222 22 6 222 36 11 222 52 0 222 115 6 222 208 26 222 447 0 222 455 0 223 14 15 223 34 20 223 53 3 223 115 13 223 162 13 223 247 0 223 477 0 224 13 24 224 19 1 224 40 30 224 91 17 224 153 15 224 226 29 224 268 0 224 276 0 225 18 3 225 52 19 225 79 22 225 144 2 225 209 18 225 298 0 225 306 0 226 26 23 226 42 13 226 82 3 226 159 10 226 203 0 226 328 0 226 336 0 227 4 27 227 20 1 227 47 25 227 58 5 227 111 21 227 182 31 227 358 0 227 366 0 228 2 13 228 31 21 228 38 7 228 62 29 228 144 9 228 236 8 228 388 0 228 396 0 229 6 3 229 8 6 229 33 29 229 52 7 229 164 23 229 217 0 229 418 0 229 426 0 230 22 31 230 24 29 230 50 1 230 105 11 230 169 5 230 448 0 230 456 0 231 15 15 231 35 20 231 54 3 231 116 13 231 163 13 231 240 1 231 478 0 232 14 24 232 20 1 232 41 30 232 92 17 232 154 15 232 227 29 232 269 0 232 277 0 233 19 3 233 53 19 233 72 23 233 145 2 233 210 18 233 299 0 233 307 0 234 27 23 234 43 13 234 83 3 234 152 11 234 204 0 234 329 0 234 337 0 235 5 27 235 21 1 235 40 26 235 59 5 235 104 22 235 183 31 235 359 0 235 367 0 236 3 13 236 24 22 236 39 7 236 63 29 236 145 9 236 237 8 236 389 0 236 397 0 237 7 3 237 9 6 237 34 29 237 53 7 237 165 23 237 218 0 237 419 0 237 427 0 238 23 31 238 25 29 238 51 1 238 106 11 238 170 5 238 449 0 238 457 0 239 8 16 239 36 20 239 55 3 239 117 13 239 164 13 239 241 1 239 479 0

APPENDIX TABLE D Specification of the base matrix B_(3/5) for the rate-⅗ LDPC code 0 14 3 0 31 8 0 33 31 0 53 13 0 77 10 0 114 22 0 162 17 0 219 27 0 283 3 0 288 0 0 296 0 1 2 24 1 30 3 1 44 23 1 66 17 1 119 31 1 167 16 1 215 5 1 277 15 1 312 0 1 320 0 2 7 21 2 16 12 2 38 4 2 58 9 2 96 30 2 151 25 2 198 23 2 260 2 2 336 0 2 344 0 3 7 27 3 22 1 3 41 6 3 59 20 3 96 12 3 146 3 3 192 26 3 250 16 3 360 0 3 368 0 4 17 3 4 28 1 4 43 8 4 66 23 4 92 17 4 128 6 4 180 5 4 289 0 4 384 0 4 392 0 5 7 4 5 9 29 5 33 13 5 42 3 5 95 19 5 130 0 5 171 21 5 281 8 5 408 0 5 416 0 6 19 16 6 33 28 6 46 28 6 77 0 6 138 24 6 174 3 6 239 8 6 432 0 6 440 0 7 9 11 7 25 16 7 52 1 7 73 20 7 136 30 7 188 22 7 227 27 7 456 0 7 464 0 8 15 3 8 24 9 8 34 31 8 54 13 8 78 10 8 115 22 8 163 17 8 220 27 8 284 3 8 289 0 8 297 0 9 3 24 9 31 3 9 45 23 9 67 17 9 112 0 9 160 17 9 208 6 9 278 15 9 313 0 9 321 0 10 0 22 10 17 12 10 39 4 10 59 9 10 97 30 10 144 26 10 199 23 10 261 2 10 337 0 10 345 0 11 0 28 11 23 1 11 42 6 11 60 20 11 97 12 11 147 3 11 193 26 11 251 16 11 361 0 11 369 0 12 18 3 12 29 1 12 44 8 12 67 23 12 93 17 12 129 6 12 181 5 12 290 0 12 385 0 12 393 0 13 0 5 13 10 29 13 34 13 13 43 3 13 88 20 13 131 0 13 172 21 13 282 8 13 409 0 13 417 0 14 20 16 14 34 28 14 47 28 14 78 0 14 139 24 14 175 3 14 232 9 14 433 0 14 441 0 15 10 11 15 26 16 15 53 1 15 74 20 15 137 30 15 189 22 15 228 27 15 457 0 15 465 0 16 8 4 16 25 9 16 35 31 16 55 13 16 79 10 16 116 22 16 164 17 16 221 27 16 285 3 16 290 0 16 298 0 17 4 24 17 24 4 17 46 23 17 68 17 17 113 0 17 161 17 17 209 6 17 279 15 17 314 0 17 322 0 18 1 22 18 18 12 18 32 5 18 60 9 18 98 30 18 145 26 18 192 24 18 262 2 18 338 0 18 346 0 19 1 28 19 16 2 19 43 6 19 61 20 19 98 12 19 148 3 19 194 26 19 252 16 19 362 0 19 370 0 20 19 3 20 30 1 20 45 8 20 68 23 20 94 17 20 130 6 20 182 5 20 291 0 20 386 0 20 394 0 21 1 5 21 11 29 21 35 13 21 44 3 21 89 20 21 132 0 21 173 21 21 283 8 21 410 0 21 418 0 22 21 16 22 35 28 22 40 29 22 79 0 22 140 24 22 168 4 22 233 9 22 434 0 22 442 0 23 11 11 23 27 16 23 54 1 23 75 20 23 138 30 23 190 22 23 229 27 23 458 0 23 466 0 24 9 4 24 26 9 24 36 31 24 48 14 24 72 11 24 117 22 24 165 17 24 222 27 24 286 3 24 291 0 24 299 0 25 5 24 25 25 4 25 47 23 25 69 17 25 114 0 25 162 17 25 210 6 25 272 16 25 315 0 25 323 0 26 2 22 26 19 12 26 33 5 26 61 9 26 99 30 26 146 26 26 193 24 26 263 2 26 339 0 26 347 0 27 2 28 27 17 2 27 44 6 27 62 20 27 99 12 27 149 3 27 195 26 27 253 16 27 363 0 27 371 0 28 20 3 28 31 1 28 46 8 28 69 23 28 95 17 28 131 6 28 183 5 28 292 0 28 387 0 28 395 0 29 2 5 29 12 29 29 36 13 29 45 3 29 90 20 29 133 0 29 174 21 29 284 8 29 411 0 29 419 0 30 22 16 30 36 28 30 41 29 30 72 1 30 141 24 30 169 4 30 234 9 30 435 0 30 443 0 31 12 11 31 28 16 31 55 1 31 76 20 31 139 30 31 191 22 31 230 27 31 459 0 31 467 0 32 10 4 32 27 9 32 37 31 32 49 14 32 73 11 32 118 22 32 166 17 32 223 27 32 287 3 32 292 0 32 300 0 33 6 24 33 26 4 33 40 24 33 70 17 33 115 0 33 163 17 33 211 6 33 273 16 33 316 0 33 324 0 34 3 22 34 20 12 34 34 5 34 62 9 34 100 30 34 147 26 34 194 24 34 256 3 34 340 0 34 348 0 35 3 28 35 18 2 35 45 6 35 63 20 35 100 12 35 150 3 35 196 26 35 254 16 35 364 0 35 372 0 36 21 3 36 24 2 36 47 8 36 70 23 36 88 18 36 132 6 36 176 6 36 293 0 36 388 0 36 396 0 37 3 5 37 13 29 37 37 13 37 46 3 37 91 20 37 134 0 37 175 21 37 285 8 37 412 0 37 420 0 38 23 16 38 37 28 38 42 29 38 73 1 38 142 24 38 170 4 38 235 9 38 436 0 38 444 0 39 13 11 39 29 16 39 48 2 39 77 20 39 140 30 39 184 23 39 231 27 39 460 0 39 468 0 40 11 4 40 28 9 40 38 31 40 50 14 40 74 11 40 119 22 40 167 17 40 216 28 40 280 4 40 293 0 40 301 0 41 7 24 41 27 4 41 41 24 41 71 17 41 116 0 41 164 17 41 212 6 41 274 16 41 317 0 41 325 0 42 4 22 42 21 12 42 35 5 42 63 9 42 101 30 42 148 26 42 195 24 42 257 3 42 341 0 42 349 0 43 4 28 43 19 2 43 46 6 43 56 21 43 101 12 43 151 3 43 197 26 43 255 16 43 365 0 43 373 0 44 22 3 44 25 2 44 40 9 44 71 23 44 89 18 44 133 6 44 177 6 44 294 0 44 389 0 44 397 0 45 4 5 45 14 29 45 38 13 45 47 3 45 92 20 45 135 0 45 168 22 45 286 8 45 413 0 45 421 0 46 16 17 46 38 28 46 43 29 46 74 1 46 143 24 46 171 4 46 236 9 46 437 0 46 445 0 47 14 11 47 30 16 47 49 2 47 78 20 47 141 30 47 185 23 47 224 28 47 461 0 47 469 0 48 12 4 48 29 9 48 39 31 48 51 14 48 75 11 48 112 23 48 160 18 48 217 28 48 281 4 48 294 0 48 302 0 49 0 25 49 28 4 49 42 24 49 64 18 49 117 0 49 165 17 49 213 6 49 275 16 49 318 0 49 326 0 50 5 22 50 22 12 50 36 5 50 56 10 50 102 30 50 149 26 50 196 24 50 258 3 50 342 0 50 350 0 51 5 28 51 20 2 51 47 6 51 57 21 51 102 12 51 144 4 51 198 26 51 248 17 51 366 0 51 374 0 52 23 3 52 26 2 52 41 9 52 64 24 52 90 18 52 134 6 52 178 6 52 295 0 52 390 0 52 398 0 53 5 5 53 15 29 53 39 13 53 40 4 53 93 20 53 128 1 53 169 22 53 287 8 53 414 0 53 422 0 54 17 17 54 39 28 54 44 29 54 75 1 54 136 25 54 172 4 54 237 9 54 438 0 54 446 0 55 15 11 55 31 16 55 50 2 55 79 20 55 142 30 55 186 23 55 225 28 55 462 0 55 470 0 56 13 4 56 30 9 56 32 0 56 52 14 56 76 11 56 113 23 56 161 18 56 218 28 56 282 4 56 295 0 56 303 0 57 1 25 57 29 4 57 43 24 57 65 18 57 118 0 57 166 17 57 214 6 57 276 16 57 319 0 57 327 0 58 6 22 58 23 12 58 37 5 58 57 10 58 103 30 58 150 26 58 197 24 58 259 3 58 343 0 58 351 0 59 6 28 59 21 2 59 40 7 59 58 21 59 103 12 59 145 4 59 199 26 59 249 17 59 367 0 59 375 0 60 16 4 60 27 2 60 42 9 60 65 24 60 91 18 60 135 6 60 179 6 60 288 1 60 391 0 60 399 0 61 6 5 61 8 30 61 32 14 61 41 4 61 94 20 61 129 1 61 170 22 61 280 9 61 415 0 61 423 0 62 18 17 62 32 29 62 45 29 62 76 1 62 137 25 62 173 4 62 238 9 62 439 0 62 447 0 63 8 12 63 24 17 63 51 2 63 72 21 63 143 30 63 187 23 63 226 28 63 463 0 63 471 0 64 15 14 64 24 26 64 39 24 64 65 9 64 118 0 64 162 5 64 220 8 64 277 2 64 296 0 64 304 0 65 0 5 65 25 19 65 47 23 65 62 23 65 116 22 65 165 23 65 203 9 65 286 24 65 320 0 65 328 0 66 6 24 66 8 6 66 20 0 66 39 16 66 49 20 66 88 30 66 146 20 66 217 24 66 258 21 66 344 0 66 352 0 67 6 0 67 21 13 67 47 22 67 48 10 67 81 16 67 141 2 67 186 6 67 249 1 67 368 0 67 376 0 68 15 20 68 34 12 68 50 18 68 79 22 68 152 23 68 179 7 68 243 4 68 392 0 68 400 0 69 8 12 69 34 21 69 52 16 69 82 16 69 127 8 69 183 12 69 232 10 69 416 0 69 424 0 70 19 21 70 33 7 70 50 14 70 105 15 70 130 30 70 208 3 70 270 24 70 440 0 70 448 0 71 2 21 71 15 1 71 29 20 71 49 0 71 86 28 71 126 8 71 228 1 71 241 29 71 464 0 71 472 0 72 8 15 72 25 26 72 32 25 72 66 9 72 119 0 72 163 5 72 221 8 72 278 2 72 297 0 72 305 0 73 1 5 73 26 19 73 40 24 73 63 23 73 117 22 73 166 23 73 204 9 73 287 24 73 321 0 73 329 0 74 7 24 74 9 6 74 21 0 74 32 17 74 50 20 74 89 30 74 147 20 74 218 24 74 259 21 74 345 0 74 353 0 75 7 0 75 22 13 75 40 23 75 49 10 75 82 16 75 142 2 75 187 6 75 250 1 75 369 0 75 377 0 76 8 21 76 35 12 76 51 18 76 72 23 76 153 23 76 180 7 76 244 4 76 393 0 76 401 0 77 9 12 77 35 21 77 53 16 77 83 16 77 120 9 77 176 13 77 233 10 77 417 0 77 425 0 78 20 21 78 34 7 78 51 14 78 106 15 78 131 30 78 209 3 78 271 24 78 441 0 78 449 0 79 3 21 79 8 2 79 30 20 79 50 0 79 87 28 79 127 8 79 229 1 79 242 29 79 465 0 79 473 0 80 9 15 80 26 26 80 33 25 80 67 9 80 112 1 80 164 5 80 222 8 80 279 2 80 298 0 80 306 0 81 2 5 81 27 19 81 41 24 81 56 24 81 118 22 81 167 23 81 205 9 81 280 25 81 322 0 81 330 0 82 0 25 82 10 6 82 22 0 82 33 17 82 51 20 82 90 30 82 148 20 82 219 24 82 260 21 82 346 0 82 354 0 83 0 1 83 23 13 83 41 23 83 50 10 83 83 16 83 143 2 83 188 6 83 251 1 83 370 0 83 378 0 84 9 21 84 36 12 84 52 18 84 73 23 84 154 23 84 181 7 84 245 4 84 394 0 84 402 0 85 10 12 85 36 21 85 54 16 85 84 16 85 121 9 85 177 13 85 234 10 85 418 0 85 426 0 86 21 21 86 35 7 86 52 14 86 107 15 86 132 30 86 210 3 86 264 25 86 442 0 86 450 0 87 4 21 87 9 2 87 31 20 87 51 0 87 80 29 87 120 9 87 230 1 87 243 29 87 466 0 87 474 0 88 10 15 88 27 26 88 34 25 88 68 9 88 113 1 88 165 5 88 223 8 88 272 3 88 299 0 88 307 0 89 3 5 89 28 19 89 42 24 89 57 24 89 119 22 89 160 24 89 206 9 89 281 25 89 323 0 89 331 0 90 1 25 90 11 6 90 23 0 90 34 17 90 52 20 90 91 30 90 149 20 90 220 24 90 261 21 90 347 0 90 355 0 91 1 1 91 16 14 91 42 23 91 51 10 91 84 16 91 136 3 91 189 6 91 252 1 91 371 0 91 379 0 92 10 21 92 37 12 92 53 18 92 74 23 92 155 23 92 182 7 92 246 4 92 395 0 92 403 0 93 11 12 93 37 21 93 55 16 93 85 16 93 122 9 93 178 13 93 235 10 93 419 0 93 427 0 94 22 21 94 36 7 94 53 14 94 108 15 94 133 30 94 211 3 94 265 25 94 443 0 94 451 0 95 5 21 95 10 2 95 24 21 95 52 0 95 81 29 95 121 9 95 231 1 95 244 29 95 467 0 95 475 0 96 11 15 96 28 26 96 35 25 96 69 9 96 114 1 96 166 5 96 216 9 96 273 3 96 300 0 96 308 0 97 4 5 97 29 19 97 43 24 97 58 24 97 112 23 97 161 24 97 207 9 97 282 25 97 324 0 97 332 0 98 2 25 98 12 6 98 16 1 98 35 17 98 53 20 98 92 30 98 150 20 98 221 24 98 262 21 98 348 0 98 356 0 99 2 1 99 17 14 99 43 23 99 52 10 99 85 16 99 137 3 99 190 6 99 253 1 99 372 0 99 380 0 100 11 21 100 38 12 100 54 18 100 75 23 100 156 23 100 183 7 100 247 4 100 396 0 100 404 0 101 12 12 101 38 21 101 48 17 101 86 16 101 123 9 101 179 13 101 236 10 101 420 0 101 428 0 102 23 21 102 37 7 102 54 14 102 109 15 102 134 30 102 212 3 102 266 25 102 444 0 102 452 0 103 6 21 103 11 2 103 25 21 103 53 0 103 82 29 103 122 9 103 224 2 103 245 29 103 468 0 103 476 0 104 12 15 104 29 26 104 36 25 104 70 9 104 115 1 104 167 5 104 217 9 104 274 3 104 301 0 104 309 0 105 5 5 105 30 19 105 44 24 105 59 24 105 113 23 105 162 24 105 200 10 105 283 25 105 325 0 105 333 0 106 3 25 106 13 6 106 17 1 106 36 17 106 54 20 106 93 30 106 151 20 106 222 24 106 263 21 106 349 0 106 357 0 107 3 1 107 18 14 107 44 23 107 53 10 107 86 16 107 138 3 107 191 6 107 254 1 107 373 0 107 381 0 108 12 21 108 39 12 108 55 18 108 76 23 108 157 23 108 176 8 108 240 5 108 397 0 108 405 0 109 13 12 109 39 21 109 49 17 109 87 16 109 124 9 109 180 13 109 237 10 109 421 0 109 429 0 110 16 22 110 38 7 110 55 14 110 110 15 110 135 30 110 213 3 110 267 25 110 445 0 110 453 0 111 7 21 111 12 2 111 26 21 111 54 0 111 83 29 111 123 9 111 225 2 111 246 29 111 469 0 111 477 0 112 13 15 112 30 26 112 37 25 112 71 9 112 116 1 112 160 6 112 218 9 112 275 3 112 302 0 112 310 0 113 6 5 113 31 19 113 45 24 113 60 24 113 114 23 113 163 24 113 201 10 113 284 25 113 326 0 113 334 0 114 4 25 114 14 6 114 18 1 114 37 17 114 55 20 114 94 30 114 144 21 114 223 24 114 256 22 114 350 0 114 358 0 115 4 1 115 19 14 115 45 23 115 54 10 115 87 16 115 139 3 115 184 7 115 255 1 115 374 0 115 382 0 116 13 21 116 32 13 116 48 19 116 77 23 116 158 23 116 177 8 116 241 5 116 398 0 116 406 0 117 14 12 117 32 22 117 50 17 117 80 17 117 125 9 117 181 13 117 238 10 117 422 0 117 430 0 118 17 22 118 39 7 118 48 15 118 111 15 118 128 31 118 214 3 118 268 25 118 446 0 118 454 0 119 0 22 119 13 2 119 27 21 119 55 0 119 84 29 119 124 9 119 226 2 119 247 29 119 470 0 119 478 0 120 14 15 120 31 26 120 38 25 120 64 10 120 117 1 120 161 6 120 219 9 120 276 3 120 303 0 120 311 0 121 7 5 121 24 20 121 46 24 121 61 24 121 115 23 121 164 24 121 202 10 121 285 25 121 327 0 121 335 0 122 5 25 122 15 6 122 19 1 122 38 17 122 48 21 122 95 30 122 145 21 122 216 25 122 257 22 122 351 0 122 359 0 123 5 1 123 20 14 123 46 23 123 55 10 123 80 17 123 140 3 123 185 7 123 248 2 123 375 0 123 383 0 124 14 21 124 33 13 124 49 19 124 78 23 124 159 23 124 178 8 124 242 5 124 399 0 124 407 0 125 15 12 125 33 22 125 51 17 125 81 17 125 126 9 125 182 13 125 239 10 125 423 0 125 431 0 126 18 22 126 32 8 126 49 15 126 104 16 126 129 31 126 215 3 126 269 25 126 447 0 126 455 0 127 1 22 127 14 2 127 28 21 127 48 1 127 85 29 127 125 9 127 227 2 127 240 30 127 471 0 127 479 0 128 0 9 128 26 28 128 45 19 128 71 8 128 105 20 128 158 18 128 209 15 128 266 31 128 304 0 128 312 0 129 5 3 129 19 30 129 24 10 129 42 25 129 56 19 129 97 6 129 156 1 129 203 3 129 261 20 129 328 0 129 336 0 130 6 17 130 17 7 130 31 18 130 44 9 130 95 0 130 171 20 130 189 14 130 275 21 130 352 0 130 360 0 131 22 10 131 29 2 131 54 14 131 126 19 131 157 6 131 179 3 131 242 11 131 376 0 131 384 0 132 12 1 132 39 13 132 48 5 132 103 6 132 137 0 132 205 28 132 235 16 132 400 0 132 408 0 133 15 4 133 17 15 133 36 11 133 41 1 133 108 6 133 150 21 133 199 22 133 255 16 133 424 0 133 432 0 134 10 6 134 20 7 134 30 1 134 50 29 134 109 17 134 135 17 134 191 30 134 267 9 134 448 0 134 456 0 135 7 6 135 12 0 135 37 30 135 44 22 135 52 29 135 80 18 135 122 6 135 168 31 135 225 26 135 290 0 135 472 0 136 1 9 136 27 28 136 46 19 136 64 9 136 106 20 136 159 18 136 210 15 136 267 31 136 305 0 136 313 0 137 6 3 137 20 30 137 25 10 137 43 25 137 57 19 137 98 6 137 157 1 137 204 3 137 262 20 137 329 0 137 337 0 138 7 17 138 18 7 138 24 19 138 45 9 138 88 1 138 172 20 138 190 14 138 276 21 138 353 0 138 361 0 139 23 10 139 30 2 139 55 14 139 127 19 139 158 6 139 180 3 139 243 11 139 377 0 139 385 0 140 13 1 140 32 14 140 49 5 140 96 7 140 138 0 140 206 28 140 236 16 140 401 0 140 409 0 141 8 5 141 18 15 141 37 11 141 42 1 141 109 6 141 151 21 141 192 23 142 248 17 141 425 0 141 433 0 142 11 6 142 21 7 142 31 1 142 51 29 142 110 17 142 128 18 142 184 31 142 268 9 142 449 0 142 457 0 143 0 7 143 13 0 143 38 30 143 45 22 143 53 29 143 81 18 143 123 6 143 169 31 143 226 26 143 291 0 143 473 0 144 2 9 144 28 28 144 47 19 144 65 9 144 107 20 144 152 19 144 211 15 144 268 31 144 306 0 144 314 0 145 7 3 145 21 30 145 26 10 145 44 25 145 58 19 145 99 6 145 158 1 145 205 3 145 263 20 145 330 0 145 338 0 146 0 18 146 19 7 146 25 19 146 46 9 146 89 1 146 173 20 146 191 14 146 277 21 146 354 0 146 362 0 147 16 11 147 31 2 147 48 15 147 120 20 147 159 6 147 181 3 147 244 11 147 378 0 147 386 0 148 14 1 148 33 14 148 50 5 148 97 7 148 139 0 148 207 28 148 237 16 148 402 0 148 410 0 149 9 5 149 19 15 149 38 11 149 43 1 149 110 6 149 144 22 149 193 23 149 249 17 149 426 0 149 434 0 150 12 6 150 22 7 150 24 2 150 52 29 150 111 17 150 129 18 150 185 31 150 269 9 150 450 0 150 458 0 151 1 7 151 14 0 151 39 30 151 46 22 151 54 29 151 82 18 151 124 6 151 170 31 151 227 26 151 292 0 151 474 0 152 3 9 152 29 28 152 40 20 152 66 9 152 108 20 152 153 19 152 212 15 152 269 31 152 307 0 152 315 0 153 0 4 153 22 30 153 27 10 153 45 25 153 59 19 153 100 6 153 159 1 153 206 3 153 256 21 153 331 0 153 339 0 154 1 18 154 20 7 154 26 19 154 47 9 154 90 1 154 174 20 154 184 15 154 278 21 154 355 0 154 363 0 155 17 11 155 24 3 155 49 15 155 121 20 155 152 7 155 182 3 155 245 11 155 379 0 155 387 0 156 15 1 156 34 14 156 51 5 156 98 7 156 140 0 156 200 29 156 238 16 156 403 0 156 411 0 157 10 5 157 20 15 157 39 11 157 44 1 157 111 6 157 145 22 157 194 23 157 250 17 157 427 0 157 435 0 158 13 6 158 23 7 158 25 2 158 53 29 158 104 18 158 130 18 158 186 31 158 270 9 158 451 0 158 459 0 159 2 7 159 15 0 159 32 31 159 47 22 159 55 29 159 83 18 159 125 6 159 171 31 159 228 26 159 293 0 159 475 0 160 4 9 160 30 28 160 41 20 160 67 9 160 109 20 160 154 19 160 213 15 160 270 31 160 308 0 160 316 0 161 1 4 161 23 30 161 28 10 161 46 25 161 60 19 161 101 6 161 152 2 161 207 3 161 257 21 161 332 0 161 340 0 162 2 18 162 21 7 162 27 19 162 40 10 162 91 1 162 175 20 162 185 15 162 279 21 162 356 0 162 364 0 163 18 11 163 25 3 163 50 15 163 122 20 163 153 7 163 183 3 163 246 11 163 380 0 163 388 0 164 8 2 164 35 14 164 52 5 164 99 7 164 141 0 164 201 29 164 239 16 164 404 0 164 412 0 165 11 5 165 21 15 165 32 12 165 45 1 165 104 7 165 146 22 165 195 23 165 251 17 165 428 0 165 436 0 166 14 6 166 16 8 166 26 2 166 54 29 166 105 18 166 131 18 166 187 31 166 271 9 166 452 0 166 460 0 167 3 7 167 8 1 167 33 31 167 40 23 167 48 30 167 84 18 167 126 6 167 172 31 167 229 26 167 294 0 167 476 0 168 5 9 168 31 28 168 42 20 168 68 9 168 110 20 168 155 19 168 214 15 168 271 31 168 309 0 168 317 0 169 2 4 169 16 31 169 29 10 169 47 25 169 61 19 169 102 6 169 153 2 169 200 4 169 258 21 169 333 0 169 341 0 170 3 18 170 22 7 170 28 19 170 41 10 170 92 1 170 168 21 170 186 15 170 272 22 170 357 0 170 365 0 171 19 11 171 26 3 171 51 15 171 123 20 171 154 7 171 176 4 171 247 11 171 381 0 171 389 0 172 9 2 172 36 14 172 53 5 172 100 7 172 142 0 172 202 29 172 232 17 172 405 0 172 413 0 173 12 5 173 22 15 173 33 12 173 46 1 173 105 7 173 147 22 173 196 23 173 252 17 173 429 0 173 437 0 174 15 6 174 17 8 174 27 2 174 55 29 174 106 18 174 132 18 174 188 31 174 264 10 174 453 0 174 461 0 175 4 7 175 9 1 175 34 31 175 41 23 175 49 30 175 85 18 175 127 6 175 173 31 175 230 26 175 295 0 175 477 0 176 6 9 176 24 29 176 43 20 176 69 9 176 111 20 176 156 19 176 215 15 176 264 0 176 310 0 176 318 0 177 3 4 177 17 31 177 30 10 177 40 26 177 62 19 177 103 6 177 154 2 177 201 4 177 259 21 177 334 0 177 342 0 178 4 18 178 23 7 178 29 19 178 42 10 178 93 1 178 169 21 178 187 15 178 273 22 178 358 0 178 366 0 179 20 11 179 27 3 179 52 15 179 124 20 179 155 7 179 177 4 179 240 12 179 382 0 179 390 0 180 10 2 180 37 14 180 54 5 180 101 7 180 143 0 180 203 29 180 233 17 180 406 0 180 414 0 181 13 5 181 23 15 181 34 12 181 47 1 181 106 7 181 148 22 181 197 23 181 253 17 181 430 0 181 438 0 182 8 7 182 18 8 182 28 2 182 48 30 182 107 18 182 133 18 182 189 31 182 265 10 182 454 0 182 462 0 183 5 7 183 10 1 183 35 31 183 42 23 183 50 30 183 86 18 183 120 7 183 174 31 183 231 26 183 288 1 183 478 0 184 7 9 184 25 29 184 44 20 184 70 9 184 104 21 184 157 19 184 208 16 184 265 0 184 311 0 184 319 0 185 4 4 185 18 31 185 31 10 185 41 26 185 63 19 185 96 7 185 155 2 185 202 4 185 260 21 185 335 0 185 343 0 186 5 18 186 16 8 186 30 19 186 43 10 186 94 1 186 170 21 186 188 15 186 274 22 186 359 0 186 367 0 187 21 11 187 28 3 187 53 15 187 125 20 187 156 7 187 178 4 187 241 12 187 383 0 187 391 0 188 11 2 188 38 14 188 55 5 188 102 7 188 136 1 188 204 29 188 234 17 188 407 0 188 415 0 189 14 5 189 16 16 189 35 12 189 40 2 189 107 7 189 149 22 189 198 23 189 254 17 189 431 0 189 439 0 190 9 7 190 19 8 190 29 2 190 49 30 190 108 18 190 134 18 190 190 31 190 266 10 190 455 0 190 463 0 191 6 7 191 11 1 191 36 31 191 43 23 191 51 30 191 87 18 191 121 7 191 175 31 191 224 27 191 289 1 191 479 0

APPENDIX TABLE E Specification of the base matrix B_(2/3) for the rate-⅔ LDPC code 0 6 31 0 13 26 0 38 22 0 43 5 0 74 9 0 83 4 0 120 16 0 162 5 0 211 28 0 259 16 0 314 3 0 320 0 0 328 0 1 0 23 1 8 27 1 31 7 1 47 5 1 78 19 1 119 17 1 154 29 1 202 14 1 240 19 1 297 2 1 340 0 1 348 0 2 0 4 2 9 15 2 30 12 2 46 31 2 66 22 2 117 2 2 170 15 2 192 29 2 258 28 2 291 27 2 360 0 2 368 0 3 5 2 3 11 7 3 28 18 3 34 5 3 94 28 3 106 2 3 156 23 3 197 21 3 265 1 3 305 5 3 380 0 3 388 0 4 23 16 4 28 19 4 35 5 4 54 11 4 86 18 4 101 23 4 148 7 4 181 3 4 237 26 4 321 0 4 400 0 4 408 0 5 0 17 5 17 28 5 26 27 5 37 29 5 61 0 5 128 30 5 150 1 5 177 0 5 223 0 5 316 8 5 420 0 5 428 0 6 8 17 6 16 3 6 41 15 6 55 3 6 129 20 6 163 28 6 206 12 6 248 14 6 302 4 6 440 0 6 448 0 7 14 19 7 22 30 7 35 19 7 60 15 7 94 9 7 179 11 7 184 14 7 237 2 7 286 11 7 460 0 7 468 0 8 7 31 8 14 26 8 39 22 8 44 5 8 75 9 8 84 4 8 121 16 8 163 5 8 212 28 8 260 16 8 315 3 8 321 0 8 329 0 9 1 23 9 9 27 9 24 8 9 40 6 9 79 19 9 112 18 9 155 29 9 203 14 9 241 19 9 298 2 9 341 0 9 349 0 10 1 4 10 10 15 10 31 12 10 47 31 10 67 22 10 118 2 10 171 15 10 193 29 10 259 28 10 292 27 10 361 0 10 369 0 11 6 2 11 12 7 11 29 18 11 35 5 11 95 28 11 107 2 11 157 23 11 198 21 11 266 1 11 306 5 11 381 0 11 389 0 12 16 17 12 29 19 12 36 5 12 55 11 12 87 18 12 102 23 12 149 7 12 182 3 12 238 26 12 322 0 12 401 0 12 409 0 13 1 17 13 18 28 13 27 27 13 38 29 13 62 0 13 129 30 13 151 1 13 178 0 13 216 1 13 317 8 13 421 0 13 429 0 14 9 17 14 17 3 14 42 15 14 48 4 14 130 20 14 164 28 14 207 12 14 249 14 14 303 4 14 441 0 14 449 0 15 15 19 15 23 30 15 36 19 15 61 15 15 95 9 15 180 11 15 185 14 15 238 2 15 287 11 15 461 0 15 469 0 16 0 0 16 15 26 16 32 23 16 45 5 16 76 9 16 85 4 16 122 16 16 164 5 16 213 28 16 261 16 16 316 3 16 322 0 16 330 0 17 2 23 17 10 27 17 25 8 17 41 6 17 72 20 17 113 18 17 156 29 17 204 14 17 242 19 17 299 2 17 342 0 17 350 0 18 2 4 18 11 15 18 24 13 18 40 0 18 68 22 18 119 2 18 172 15 18 194 29 18 260 28 18 293 27 18 362 0 18 370 0 19 7 2 19 13 7 19 30 18 19 36 5 19 88 29 19 108 2 19 158 23 19 199 21 19 267 1 19 307 5 19 382 0 19 390 0 20 17 17 20 30 19 20 37 5 20 48 12 20 80 19 20 103 23 20 150 7 20 183 3 20 239 26 20 323 0 20 402 0 20 410 0 21 2 17 21 19 28 21 28 27 21 39 29 21 63 0 21 130 30 21 144 2 21 179 0 21 217 1 21 318 8 21 422 0 21 430 0 22 10 17 22 18 3 22 43 15 22 49 4 22 131 20 22 165 28 22 200 13 22 250 14 22 296 5 22 442 0 22 450 0 23 8 20 23 16 31 23 37 19 23 62 15 23 88 10 23 181 11 23 186 14 23 239 2 23 280 12 23 462 0 23 470 0 24 1 0 24 8 27 24 33 23 24 46 5 24 77 9 24 86 4 24 123 16 24 165 5 24 214 28 24 262 16 24 317 3 24 323 0 24 331 0 25 3 23 25 11 27 25 26 8 25 42 6 25 73 20 25 114 18 25 157 29 25 205 14 25 243 19 25 300 2 25 343 0 25 351 0 26 3 4 26 12 15 26 25 13 26 41 0 26 69 22 26 112 3 26 173 15 26 195 29 26 261 28 26 294 27 26 363 0 26 371 0 27 0 3 27 14 7 27 31 18 27 37 5 27 89 29 27 109 2 27 159 23 27 192 22 27 268 1 27 308 5 27 383 0 27 391 0 28 18 17 28 31 19 28 38 5 28 49 12 28 81 19 28 96 24 28 151 7 28 176 4 28 232 27 28 324 0 28 403 0 28 411 0 29 3 17 29 20 28 29 29 27 29 32 30 29 56 1 29 131 30 29 145 2 29 180 0 29 218 1 29 319 8 29 423 0 29 431 0 30 11 17 30 19 3 30 44 15 30 50 4 30 132 20 30 166 28 30 201 13 30 251 14 30 297 5 30 443 0 30 451 0 31 9 20 31 17 31 31 38 19 31 63 15 31 89 10 31 182 11 31 187 14 31 232 3 31 281 12 31 463 0 31 471 0 32 2 0 32 9 27 32 34 23 32 47 5 32 78 9 32 87 4 32 124 16 32 166 5 32 215 28 32 263 16 32 318 3 32 324 0 32 332 0 33 1 5 33 14 30 33 29 21 33 47 1 33 76 15 33 127 23 33 154 7 33 192 3 33 246 23 33 317 24 33 344 0 33 352 0 34 4 4 34 13 15 34 26 13 34 42 0 34 70 22 34 113 3 34 174 15 34 196 29 34 262 28 34 295 27 34 364 0 34 372 0 35 4 21 35 11 18 35 17 7 35 33 30 35 74 4 35 126 29 35 153 28 35 189 30 35 242 1 35 282 31 35 384 0 35 392 0 36 19 17 36 24 20 36 39 5 36 50 12 36 82 19 36 97 24 36 144 8 36 177 4 36 233 27 36 325 0 36 404 0 36 412 0 37 21 0 37 26 6 37 33 9 37 54 14 37 91 30 37 143 15 37 175 18 37 253 10 37 273 8 37 424 0 37 432 0 38 12 17 38 20 3 38 45 15 38 51 4 38 133 20 38 167 28 38 202 13 38 252 14 38 298 5 38 444 0 38 452 0 39 19 0 39 32 25 39 40 29 39 65 11 39 80 27 39 130 5 39 175 11 39 229 3 39 274 31 39 464 0 39 472 0 40 3 0 40 10 27 40 35 23 40 40 6 40 79 9 40 80 5 40 125 16 40 167 5 40 208 29 40 256 17 40 319 3 40 325 0 40 333 0 41 2 5 41 15 30 41 30 21 41 40 2 41 77 15 41 120 24 41 155 7 41 193 3 41 247 23 41 318 24 41 345 0 41 353 0 42 5 4 42 14 15 42 27 13 42 43 0 42 71 22 42 114 3 42 175 15 42 197 29 42 263 28 42 288 28 42 365 0 42 373 0 43 5 21 43 12 18 43 18 7 43 34 30 43 75 4 43 127 29 43 154 28 43 190 30 43 243 1 43 283 31 43 385 0 43 393 0 44 20 17 44 25 20 44 32 6 44 51 12 44 83 19 44 98 24 44 145 8 44 178 4 44 234 27 44 326 0 44 405 0 44 413 0 45 22 0 45 27 6 45 34 9 45 55 14 45 92 30 45 136 16 45 168 19 45 254 10 45 274 8 45 425 0 45 433 0 46 13 17 46 21 3 46 46 15 46 52 4 46 134 20 46 160 29 46 203 13 46 253 14 46 299 5 46 445 0 46 453 0 47 20 0 47 33 25 47 41 29 47 66 11 47 81 27 47 131 5 47 168 12 47 230 3 47 275 31 47 465 0 47 473 0 48 4 0 48 11 27 48 36 23 48 41 6 48 72 10 48 81 5 48 126 16 48 160 6 48 209 29 48 257 17 48 312 4 48 326 0 48 334 0 49 3 5 49 8 31 49 31 21 49 41 2 49 78 15 49 121 24 49 156 7 49 194 3 49 240 24 49 319 24 49 346 0 49 354 0 50 6 4 50 15 15 50 28 13 50 44 0 50 64 23 50 115 3 50 168 16 50 198 29 50 256 29 50 289 28 50 366 0 50 374 0 51 6 21 51 13 18 51 19 7 51 35 30 51 76 4 51 120 30 51 155 28 51 191 30 51 244 1 51 284 31 51 386 0 51 394 0 52 21 17 52 26 20 52 33 6 52 52 12 52 84 19 52 99 24 52 146 8 52 179 4 52 235 27 52 327 0 52 406 0 52 414 0 53 23 0 53 28 6 53 35 9 53 48 15 53 93 30 53 137 16 53 169 19 53 255 10 53 275 8 53 426 0 53 434 0 54 14 17 54 22 3 54 47 15 54 53 4 54 135 20 54 161 29 54 204 13 54 254 14 54 300 5 54 446 0 54 454 0 55 21 0 55 34 25 55 42 29 55 67 11 55 82 27 55 132 5 55 169 12 55 231 3 55 276 31 55 466 0 55 474 0 56 5 0 56 12 27 56 37 23 56 42 6 56 73 10 56 82 5 56 127 16 56 161 6 56 210 29 56 258 17 56 313 4 56 327 0 56 335 0 57 4 5 57 9 31 57 24 22 57 42 2 57 79 15 57 122 24 57 157 7 57 195 3 57 241 24 57 312 25 57 347 0 57 355 0 58 7 4 58 8 16 58 29 13 58 45 0 58 65 23 58 116 3 58 169 16 58 199 29 58 257 29 58 290 28 58 367 0 58 375 0 59 7 21 59 14 18 59 20 7 59 36 30 59 77 4 59 121 30 59 156 28 59 184 31 59 245 1 59 285 31 59 387 0 59 395 0 60 22 17 60 27 20 60 34 6 60 53 12 60 85 19 60 100 24 60 147 8 60 180 4 60 236 27 60 320 1 60 407 0 60 415 0 61 16 1 61 29 6 61 36 9 61 49 15 61 94 30 61 138 16 61 170 19 61 248 11 61 276 8 61 427 0 61 435 0 62 15 17 62 23 3 62 40 16 62 54 4 62 128 21 62 162 29 62 205 13 62 255 14 62 301 5 62 447 0 62 455 0 63 22 0 63 35 25 63 43 29 63 68 11 63 83 27 63 133 5 63 170 12 63 224 4 63 277 31 63 467 0 63 475 0 64 3 21 64 11 21 64 25 23 64 41 11 64 101 13 64 121 2 64 162 2 64 201 27 64 253 24 64 311 17 64 328 0 64 336 0 65 5 5 65 10 31 65 25 22 65 43 2 65 72 16 65 123 24 65 158 7 65 196 3 65 242 24 65 313 25 65 348 0 65 356 0 66 11 28 66 26 2 66 32 29 66 45 19 66 92 11 66 111 2 66 141 31 66 196 11 66 259 5 66 288 17 66 368 0 66 376 0 67 0 22 67 15 18 67 21 7 67 37 30 67 78 4 67 122 30 67 157 28 67 185 31 67 246 1 67 286 31 67 388 0 67 396 0 68 2 11 68 18 23 68 25 14 68 38 18 68 52 15 68 103 2 68 151 27 68 182 13 68 269 11 68 309 9 68 408 0 68 416 0 69 17 1 69 30 6 69 37 9 69 50 15 69 95 30 69 139 16 69 171 19 69 249 11 69 277 8 69 428 0 69 436 0 70 13 1 70 19 1 70 43 9 70 62 5 70 108 8 70 133 24 70 169 3 70 216 19 70 301 4 70 448 0 70 456 0 71 23 0 71 36 25 71 44 29 71 69 11 71 84 27 71 134 5 71 171 12 71 225 4 71 278 31 71 468 0 71 476 0 72 4 21 72 12 21 72 26 23 72 42 11 72 102 13 72 122 2 72 163 2 72 202 27 72 254 24 72 304 18 72 329 0 72 337 0 73 6 5 73 11 31 73 26 22 73 44 2 73 73 16 73 124 24 73 159 7 73 197 3 73 243 24 73 314 25 73 349 0 73 357 0 74 12 28 74 27 2 74 33 29 74 46 19 74 93 11 74 104 3 74 142 31 74 197 11 74 260 5 74 289 17 74 369 0 74 377 0 75 1 22 75 8 19 75 22 7 75 38 30 75 79 4 75 123 30 75 158 28 75 186 31 75 247 1 75 287 31 75 389 0 75 397 0 76 3 11 76 19 23 76 26 14 76 39 18 76 53 15 76 96 3 76 144 28 76 183 13 76 270 11 76 310 9 76 409 0 76 417 0 77 18 1 77 31 6 77 38 9 77 51 15 77 88 31 77 140 16 77 172 19 77 250 11 77 278 8 77 429 0 77 437 0 78 14 1 78 20 1 78 44 9 78 63 5 78 109 8 78 134 24 78 170 3 78 217 19 78 302 4 78 449 0 78 457 0 79 16 1 79 37 25 79 45 29 79 70 11 79 85 27 79 135 5 79 172 12 79 226 4 79 279 31 79 469 0 79 477 0 80 5 21 80 13 21 80 27 23 80 43 11 80 103 13 80 123 2 80 164 2 80 203 27 80 255 24 80 305 18 80 330 0 80 338 0 81 7 5 81 12 31 81 27 22 81 45 2 81 74 16 81 125 24 81 152 8 81 198 3 81 244 24 81 315 25 81 350 0 81 358 0 82 13 28 82 28 2 82 34 29 82 47 19 82 94 11 82 105 3 82 143 31 82 198 11 82 261 5 82 290 17 82 370 0 82 378 0 83 2 22 83 9 19 83 23 7 83 39 30 83 72 5 83 124 30 83 159 28 83 187 31 83 240 2 83 280 0 83 390 0 83 398 0 84 4 11 84 20 23 84 27 14 84 32 19 84 54 15 84 97 3 84 145 28 84 176 14 84 271 11 84 311 9 84 410 0 84 418 0 85 19 1 85 24 7 85 39 9 85 52 15 85 89 31 85 141 16 85 173 19 85 251 11 85 279 8 85 430 0 85 438 0 86 15 1 86 21 1 86 45 9 86 56 6 86 110 8 86 135 24 86 171 3 86 218 19 86 303 4 86 450 0 86 458 0 87 17 1 87 38 25 87 46 29 87 71 11 87 86 27 87 128 6 87 173 12 87 227 4 87 272 0 87 470 0 87 478 0 88 6 21 88 14 21 88 28 23 88 44 11 88 96 14 88 124 2 88 165 2 88 204 27 88 248 25 88 306 18 88 331 0 88 339 0 89 0 6 89 13 31 89 28 22 89 46 2 89 75 16 89 126 24 89 153 8 89 199 3 89 245 24 89 316 25 89 351 0 89 359 0 90 14 28 90 29 2 90 35 29 90 40 20 90 95 11 90 106 3 90 136 0 90 199 11 90 262 5 90 291 17 90 371 0 90 379 0 91 3 22 91 10 19 91 16 8 91 32 31 91 73 5 91 125 30 91 152 29 91 188 31 91 241 2 91 281 0 91 391 0 91 399 0 92 5 11 92 21 23 92 28 14 92 33 19 92 55 15 92 98 3 92 146 28 92 177 14 92 264 12 92 304 10 92 411 0 92 419 0 93 20 1 93 25 7 93 32 10 93 53 15 93 90 31 93 142 16 93 174 19 93 252 11 93 272 9 93 431 0 93 439 0 94 8 2 94 22 1 94 46 9 94 57 6 94 111 8 94 128 25 94 172 3 94 219 19 94 296 5 94 451 0 94 459 0 95 18 1 95 39 25 95 47 29 95 64 12 95 87 27 95 129 6 95 174 12 95 228 4 95 273 0 95 471 0 95 479 0 96 7 21 96 15 21 96 29 23 96 45 11 96 97 14 96 125 2 96 166 2 96 205 27 96 249 25 96 307 18 96 332 0 96 340 0 97 6 8 97 10 24 97 30 23 97 41 11 97 85 3 97 114 23 97 149 25 97 212 10 97 232 24 97 295 9 97 352 0 97 360 0 98 15 28 98 30 2 98 36 29 98 41 20 98 88 12 98 107 3 98 137 0 98 192 12 98 263 5 98 292 17 98 372 0 98 380 0 99 6 29 99 17 8 99 26 19 99 38 1 99 61 28 99 117 26 99 140 23 99 187 15 99 224 15 99 286 17 99 392 0 99 400 0 100 6 11 100 22 23 100 29 14 100 34 19 100 48 16 100 99 3 100 147 28 100 178 14 100 265 12 100 305 10 100 412 0 100 420 0 101 19 11 101 35 29 101 43 8 101 66 20 101 100 1 101 165 3 101 208 13 101 224 25 101 277 2 101 432 0 101 440 0 102 9 2 102 23 1 102 47 9 102 58 6 102 104 9 102 129 25 102 173 3 102 220 19 102 297 5 102 452 0 102 460 0 103 6 4 103 18 4 103 46 23 103 64 7 103 107 13 103 143 0 103 187 30 103 223 18 103 268 25 103 322 0 103 472 0 104 0 22 104 8 22 104 30 23 104 46 11 104 98 14 104 126 2 104 167 2 104 206 27 104 250 25 104 308 18 104 333 0 104 341 0 105 7 8 105 11 24 105 31 23 105 42 11 105 86 3 105 115 23 105 150 25 105 213 10 105 233 24 105 288 10 105 353 0 105 361 0 106 8 29 106 31 2 106 37 29 106 42 20 106 89 12 106 108 3 106 138 0 106 193 12 106 256 6 106 293 17 106 373 0 106 381 0 107 7 29 107 18 8 107 27 19 107 39 1 107 62 28 107 118 26 107 141 23 107 188 15 107 225 15 107 287 17 107 393 0 107 401 0 108 7 11 108 23 23 108 30 14 108 35 19 108 49 16 108 100 3 108 148 28 108 179 14 108 266 12 108 306 10 108 413 0 108 421 0 109 20 11 109 36 29 109 44 8 109 67 20 109 101 1 109 166 3 109 209 13 109 225 25 109 278 2 109 433 0 109 441 0 110 10 2 110 16 2 110 40 10 110 59 6 110 105 9 110 130 25 110 174 3 110 221 19 110 298 5 110 453 0 110 461 0 111 7 4 111 19 4 111 47 23 111 65 7 111 108 13 111 136 1 111 188 30 111 216 19 111 269 25 111 323 0 111 473 0 112 1 22 112 9 22 112 31 23 112 47 11 112 99 14 112 127 2 112 160 3 112 207 27 112 251 25 112 309 18 112 334 0 112 342 0 113 0 9 113 12 24 113 24 24 113 43 11 113 87 3 113 116 23 113 151 25 113 214 10 113 234 24 113 289 10 113 354 0 113 362 0 114 9 29 114 24 3 114 38 29 114 43 20 114 90 12 114 109 3 114 139 0 114 194 12 114 257 6 114 294 17 114 374 0 114 382 0 115 0 30 115 19 8 115 28 19 115 32 2 115 63 28 115 119 26 115 142 23 115 189 15 115 226 15 115 280 18 115 394 0 115 402 0 116 0 12 116 16 24 116 31 14 116 36 19 116 50 16 116 101 3 116 149 28 116 180 14 116 267 12 116 307 10 116 414 0 116 422 0 117 21 11 117 37 29 117 45 8 117 68 20 117 102 1 117 167 3 117 210 13 117 226 25 117 279 2 117 434 0 117 442 0 118 11 2 118 17 2 118 41 10 118 60 6 118 106 9 118 131 25 118 175 3 118 222 19 118 299 5 118 454 0 118 462 0 119 0 5 119 20 4 119 40 24 119 66 7 119 109 13 119 137 1 119 189 30 119 217 19 119 270 25 119 324 0 119 474 0 120 2 22 120 10 22 120 24 24 120 40 12 120 100 14 120 120 3 120 161 3 120 200 28 120 252 25 120 310 18 120 335 0 120 343 0 121 1 9 121 13 24 121 25 24 121 44 11 121 80 4 121 117 23 121 144 26 121 215 10 121 235 24 121 290 10 121 355 0 121 363 0 122 10 29 122 25 3 122 39 29 122 44 20 122 91 12 122 110 3 122 140 0 122 195 12 122 258 6 122 295 17 122 375 0 122 383 0 123 1 30 123 20 8 123 29 19 123 33 2 123 56 29 123 112 27 123 143 23 123 190 15 123 227 15 123 281 18 123 395 0 123 403 0 124 1 12 124 17 24 124 24 15 124 37 19 124 51 16 124 102 3 124 150 28 124 181 14 124 268 12 124 308 10 124 415 0 124 423 0 125 22 11 125 38 29 125 46 8 125 69 20 125 103 1 125 160 4 125 211 13 125 227 25 125 272 3 125 435 0 125 443 0 126 12 2 126 18 2 126 42 10 126 61 6 126 107 9 126 132 25 126 168 4 126 223 19 126 300 5 126 455 0 126 463 0 127 1 5 127 21 4 127 41 24 127 67 7 127 110 13 127 138 1 127 190 30 127 218 19 127 271 25 127 325 0 127 475 0 128 4 22 128 12 26 128 27 7 128 43 5 128 74 19 128 115 17 128 158 28 128 206 13 128 244 18 128 301 1 128 336 0 128 344 0 129 2 9 129 14 24 129 26 24 129 45 11 129 81 4 129 118 23 129 145 26 129 208 11 129 236 24 129 291 10 129 356 0 129 364 0 130 1 2 130 15 6 130 24 18 130 38 4 130 90 28 130 110 1 130 152 23 130 193 21 130 269 0 130 309 4 130 376 0 130 384 0 131 2 30 131 21 8 131 30 19 131 34 2 131 57 29 131 113 27 131 136 24 131 191 15 131 228 15 131 282 18 131 396 0 131 404 0 132 4 16 132 21 27 132 30 26 132 33 29 132 57 0 132 132 29 132 146 1 132 181 31 132 219 0 132 312 8 132 416 0 132 424 0 133 23 11 133 39 29 133 47 8 133 70 20 133 96 2 133 161 4 133 212 13 133 228 25 133 273 3 133 436 0 133 444 0 134 10 19 134 18 30 134 39 18 134 56 15 134 90 9 134 183 10 134 188 13 134 233 2 134 282 11 134 456 0 134 464 0 135 2 5 135 22 4 135 42 24 135 68 7 135 111 13 135 139 1 135 191 30 135 219 19 135 264 26 135 326 0 135 476 0 136 5 22 136 13 26 136 28 7 136 44 5 136 75 19 136 116 17 136 159 28 136 207 13 136 245 18 136 302 1 136 337 0 136 345 0 137 3 9 137 15 24 137 27 24 137 46 11 137 82 4 137 119 23 137 146 26 137 209 11 137 237 24 137 292 10 137 357 0 137 365 0 138 2 2 138 8 7 138 25 18 138 39 4 138 91 28 138 111 1 138 153 23 138 194 21 138 270 0 138 310 4 138 377 0 138 385 0 139 3 30 139 22 8 139 31 19 139 35 2 139 58 29 139 114 27 139 137 24 139 184 16 139 229 15 139 283 18 139 397 0 139 405 0 140 5 16 140 22 27 140 31 26 140 34 29 140 58 0 140 133 29 140 147 1 140 182 31 140 220 0 140 313 8 140 417 0 140 425 0 141 16 12 141 32 30 141 40 9 141 71 20 141 97 2 141 162 4 141 213 13 141 229 25 141 274 3 141 437 0 141 445 0 142 11 19 142 19 30 142 32 19 142 57 15 142 91 9 142 176 11 142 189 13 142 234 2 142 283 11 142 457 0 142 465 0 143 3 5 143 23 4 143 43 24 143 69 7 143 104 14 143 140 1 143 184 31 143 220 19 143 265 26 143 327 0 143 477 0 144 6 22 144 14 26 144 29 7 144 45 5 144 76 19 144 117 17 144 152 29 144 200 14 144 246 18 144 303 1 144 338 0 144 346 0 145 4 9 145 8 25 145 28 24 145 47 11 145 83 4 145 112 24 145 147 26 145 210 11 145 238 24 145 293 10 145 358 0 145 366 0 146 3 2 146 9 7 146 26 18 146 32 5 146 92 28 146 104 2 146 154 23 146 195 21 146 271 0 146 311 4 146 378 0 146 386 0 147 4 30 147 23 8 147 24 20 147 36 2 147 59 29 147 115 27 147 138 24 147 185 16 147 230 15 147 284 18 147 398 0 147 406 0 148 6 16 148 23 27 148 24 27 148 35 29 148 59 0 148 134 29 148 148 1 148 183 31 148 221 0 148 314 8 148 418 0 148 426 0 149 17 12 149 33 30 149 41 9 149 64 21 149 98 2 149 163 4 149 214 13 149 230 25 149 275 3 149 438 0 149 446 0 150 12 19 150 20 30 150 33 19 150 58 15 150 92 9 150 177 11 150 190 13 150 235 2 150 284 11 150 458 0 150 466 0 151 4 5 151 16 5 151 44 24 151 70 7 151 105 14 151 141 1 151 185 31 151 221 19 151 266 26 151 320 1 151 478 0 152 7 22 152 15 26 152 30 7 152 46 5 152 77 19 152 118 17 152 153 29 152 201 14 152 247 18 152 296 2 152 339 0 152 347 0 153 5 9 153 9 25 153 29 24 153 40 12 153 84 4 153 113 24 153 148 26 153 211 11 153 239 24 153 294 10 153 359 0 153 367 0 154 4 2 154 10 7 154 27 18 154 33 5 154 93 28 154 105 2 154 155 23 154 196 21 154 264 1 154 304 5 154 379 0 154 387 0 155 5 30 155 16 9 155 25 20 155 37 2 155 60 29 155 116 27 155 139 24 155 186 16 155 231 15 155 285 18 155 399 0 155 407 0 156 7 16 156 16 28 156 25 27 156 36 29 156 60 0 156 135 29 156 149 1 156 176 0 156 222 0 156 315 8 156 419 0 156 427 0 157 18 12 157 34 30 157 42 9 157 65 21 157 99 2 157 164 4 157 215 13 157 231 25 157 276 3 157 439 0 157 447 0 158 13 19 158 21 30 158 34 19 158 59 15 158 93 9 158 178 11 158 191 13 158 236 2 158 285 11 158 459 0 158 467 0 159 5 5 159 17 5 159 45 24 159 71 7 159 106 14 159 142 1 159 186 31 159 222 19 159 267 26 159 321 1 159 479 0

APPENDIX TABLE F Specification of the base matrix B_(3/4) for the rate-¾ LDPC code 0 3 8 0 12 23 0 16 6 0 27 5 0 36 19 0 48 3 0 84 19 0 114 9 0 143 27 0 179 21 0 206 10 0 238 0 0 274 21 0 314 3 0 353 18 0 360 0 0 368 0 1 1 14 1 12 12 1 23 26 1 37 6 1 70 14 1 84 6 1 105 23 1 143 25 1 174 0 1 204 22 1 233 2 1 268 2 1 307 4 1 345 15 1 375 0 1 383 0 2 2 4 2 12 10 2 22 21 2 35 19 2 48 15 2 84 7 2 118 4 2 134 28 2 170 13 2 189 13 2 231 4 2 272 2 2 308 4 2 337 2 2 390 0 2 398 0 3 8 3 3 20 22 3 26 5 3 42 0 3 86 10 3 107 7 3 139 4 3 167 31 3 205 2 3 234 26 3 298 5 3 311 12 3 337 1 3 405 0 3 413 0 4 7 25 4 13 1 4 22 8 4 25 10 4 41 2 4 78 11 4 99 3 4 147 1 4 156 28 4 201 27 4 243 14 4 249 11 4 315 15 4 365 0 4 420 0 4 428 0 5 4 27 5 12 27 5 21 30 5 30 28 5 36 11 5 66 3 5 107 10 5 127 8 5 150 26 5 185 19 5 221 4 5 268 1 5 285 7 5 328 4 5 435 0 5 443 0 6 1 24 6 9 22 6 29 20 6 33 3 6 60 29 6 89 29 6 132 10 6 148 13 6 192 21 6 209 31 6 240 28 6 288 25 6 334 2 6 450 0 6 458 0 7 2 10 7 26 27 7 39 7 7 41 26 7 63 2 7 91 21 7 123 22 7 158 9 7 185 3 7 208 7 7 244 2 7 272 0 7 321 25 7 465 0 7 473 0 8 4 8 8 13 23 8 17 6 8 28 5 8 37 19 8 49 3 8 85 19 8 115 9 8 136 28 8 180 21 8 207 10 8 239 0 8 275 21 8 315 3 8 354 18 8 361 0 8 369 0 9 4 20 9 8 11 9 21 22 9 34 0 9 53 0 9 75 16 9 109 20 9 136 22 9 175 4 9 199 11 9 231 14 9 256 22 9 302 27 9 356 7 9 376 0 9 384 0 10 3 4 10 13 10 10 23 21 10 36 19 10 49 15 10 85 7 10 119 4 10 135 28 10 171 13 10 190 13 10 224 5 10 273 2 10 309 4 10 338 2 10 391 0 10 399 0 11 9 3 11 21 22 11 27 5 11 43 0 11 87 10 11 108 7 11 140 4 11 160 0 11 206 2 11 235 26 11 299 5 11 304 13 11 338 1 11 406 0 11 414 0 12 0 26 12 14 1 12 23 8 12 26 10 12 42 2 12 79 11 12 100 3 12 148 1 12 157 28 12 202 27 12 244 14 12 250 11 12 316 15 12 366 0 12 421 0 12 429 0 13 5 27 13 13 27 13 22 30 13 31 28 13 37 11 13 67 3 13 108 10 13 120 9 13 151 26 13 186 19 13 222 4 13 269 1 13 286 7 13 329 4 13 436 0 13 444 0 14 2 24 14 10 22 14 30 20 14 34 3 14 61 29 14 90 29 14 133 10 14 149 13 14 193 21 14 210 31 14 241 28 14 289 25 14 335 2 14 451 0 14 459 0 15 3 10 15 27 27 15 32 8 15 42 26 15 56 3 15 92 21 15 124 22 15 159 9 15 186 3 15 209 7 15 245 2 15 273 0 15 322 25 15 466 0 15 474 0 16 5 8 16 14 23 16 18 6 16 29 5 16 38 19 16 50 3 16 86 19 16 116 9 16 137 28 16 181 21 16 200 11 16 232 1 16 276 21 16 316 3 16 355 18 16 362 0 16 370 0 17 5 20 17 9 11 17 22 22 17 35 0 17 54 0 17 76 16 17 110 20 17 137 22 17 168 5 17 192 12 17 224 15 17 257 22 17 303 27 17 357 7 17 377 0 17 385 0 18 10 13 18 17 15 18 29 19 18 36 7 18 48 2 18 79 11 18 112 2 18 133 11 18 161 17 18 195 26 18 231 27 18 260 2 18 296 11 18 336 6 18 392 0 18 400 0 19 10 3 19 22 22 19 28 5 19 44 0 19 80 11 19 109 7 19 141 4 19 161 0 19 207 2 19 236 26 19 300 5 19 305 13 19 339 1 19 407 0 19 415 0 20 1 26 20 15 1 20 16 9 20 27 10 20 43 2 20 72 12 20 101 3 20 149 1 20 158 28 20 203 27 20 245 14 20 251 11 20 317 15 20 367 0 20 422 0 20 430 0 21 6 27 21 14 27 21 23 30 21 24 29 21 38 11 21 68 3 21 109 10 21 121 9 21 144 27 21 187 19 21 223 4 21 270 1 21 287 7 21 330 4 21 437 0 21 445 0 22 3 24 22 11 22 22 31 20 22 35 3 22 62 29 22 91 29 22 134 10 22 150 13 22 194 21 22 211 31 22 242 28 22 290 25 22 328 3 22 452 0 22 460 0 23 4 10 23 28 27 23 33 8 23 43 26 23 57 3 23 93 21 23 125 22 23 152 10 23 187 3 23 210 7 23 246 2 23 274 0 23 323 25 23 467 0 23 475 0 24 6 8 24 15 23 24 19 6 24 30 5 24 39 19 24 51 3 24 87 19 24 117 9 24 138 28 24 182 21 24 201 11 24 233 1 24 277 21 24 317 3 24 356 18 24 363 0 24 371 0 25 6 20 25 10 11 25 23 22 25 36 0 25 55 0 25 77 16 25 111 20 25 138 22 25 169 5 25 193 12 25 225 15 25 258 22 25 296 28 25 358 7 25 378 0 25 386 0 26 11 13 26 18 15 26 30 19 26 37 7 26 49 2 26 72 12 26 113 2 26 134 11 26 162 17 26 196 26 26 224 28 26 261 2 26 297 11 26 337 6 26 393 0 26 401 0 27 7 13 27 8 9 27 23 3 27 24 0 27 44 26 27 78 0 27 96 10 27 129 1 27 163 31 27 196 0 27 219 9 27 256 21 27 289 20 27 331 24 27 408 0 27 416 0 28 2 26 28 8 2 28 17 9 28 28 10 28 44 2 28 73 12 28 102 3 28 150 1 28 159 28 28 204 27 28 246 14 28 252 11 28 318 15 28 360 1 28 423 0 28 431 0 29 7 27 29 15 27 29 16 31 29 25 29 29 39 11 29 69 3 29 110 10 29 122 9 29 145 27 29 188 19 29 216 5 29 271 1 29 280 8 29 331 4 29 438 0 29 446 0 30 4 24 30 12 22 30 24 21 30 36 3 30 63 29 30 92 29 30 135 10 30 151 13 30 195 21 30 212 31 30 243 28 30 291 25 30 329 3 30 453 0 30 461 0 31 5 10 31 29 27 31 34 8 31 44 26 31 58 3 31 94 21 31 126 22 31 153 10 31 188 3 31 211 7 31 247 2 31 275 0 31 324 25 31 468 0 31 476 0 32 7 8 32 8 24 32 20 6 32 31 5 32 32 20 32 52 3 32 80 20 32 118 9 32 139 28 32 183 21 32 202 11 32 234 1 32 278 21 32 318 3 32 357 18 32 364 0 32 372 0 33 7 20 33 11 11 33 16 23 33 37 0 33 48 1 33 78 16 33 104 21 33 139 22 33 170 5 33 194 12 33 226 15 33 259 22 33 297 28 33 359 7 33 379 0 33 387 0 34 12 13 34 19 15 34 31 19 34 38 7 34 50 2 34 73 12 34 114 2 34 135 11 34 163 17 34 197 26 34 225 28 34 262 2 34 298 11 34 338 6 34 394 0 34 402 0 35 0 14 35 9 9 35 16 4 35 25 0 35 45 26 35 79 0 35 97 10 35 130 1 35 164 31 35 197 0 35 220 9 35 257 21 35 290 20 35 332 24 35 409 0 35 417 0 36 13 21 36 22 26 36 26 7 36 35 11 36 65 22 36 103 12 36 147 14 36 173 30 36 185 6 36 216 18 36 269 10 36 280 26 36 345 15 36 424 0 36 432 0 37 0 28 37 8 28 37 17 31 37 26 29 37 32 12 37 70 3 37 111 10 37 123 9 37 146 27 37 189 19 37 217 5 37 264 2 37 281 8 37 332 4 37 439 0 37 447 0 38 5 24 38 13 22 38 25 21 38 37 3 38 56 30 38 93 29 38 128 11 38 144 14 38 196 21 38 213 31 38 244 28 38 292 25 38 330 3 38 454 0 38 462 0 39 6 10 39 30 27 39 35 8 39 45 26 39 59 3 39 95 21 39 127 22 39 154 10 39 189 3 39 212 7 39 240 3 39 276 0 39 325 25 39 469 0 39 477 0 40 0 9 40 9 24 40 21 6 40 24 6 40 33 20 40 53 3 40 81 20 40 119 9 40 140 28 40 176 22 40 203 11 40 235 1 40 279 21 40 319 3 40 358 18 40 365 0 40 373 0 41 0 21 41 12 11 41 17 23 41 38 0 41 49 1 41 79 16 41 105 21 41 140 22 41 171 5 41 195 12 41 227 15 41 260 22 41 298 28 41 352 8 41 380 0 41 388 0 42 13 13 42 20 15 42 24 20 42 39 7 42 51 2 42 74 12 42 115 2 42 128 12 42 164 17 42 198 26 42 226 28 42 263 2 42 299 11 42 339 6 42 395 0 42 403 0 43 1 14 43 10 9 43 17 4 43 26 0 43 46 26 43 72 1 43 98 10 43 131 1 43 165 31 43 198 0 43 221 9 43 258 21 43 291 20 43 333 24 43 410 0 43 418 0 44 14 21 44 23 26 44 27 7 44 36 11 44 66 22 44 96 13 44 148 14 44 174 30 44 186 6 44 217 18 44 270 10 44 281 26 44 346 15 44 425 0 44 433 0 45 3 20 45 19 19 45 30 15 45 37 9 45 69 0 45 102 28 45 121 2 45 161 7 45 179 2 45 212 19 45 251 5 45 327 18 45 353 9 45 440 0 45 448 0 46 6 24 46 14 22 46 26 21 46 38 3 46 57 30 46 94 29 46 129 11 46 145 14 46 197 21 46 214 31 46 245 28 46 293 25 46 331 3 46 455 0 46 463 0 47 7 10 47 31 27 47 36 8 47 46 26 47 60 3 47 88 22 47 120 23 47 155 10 47 190 3 47 213 7 47 241 3 47 277 0 47 326 25 47 470 0 47 478 0 48 1 9 48 10 24 48 22 6 48 25 6 48 34 20 48 54 3 48 82 20 48 112 10 48 141 28 48 177 22 48 204 11 48 236 1 48 272 22 48 312 4 48 359 18 48 366 0 48 374 0 49 1 21 49 13 11 49 18 23 49 39 0 49 50 1 49 72 17 49 106 21 49 141 22 49 172 5 49 196 12 49 228 15 49 261 22 49 299 28 49 353 8 49 381 0 49 389 0 50 14 13 50 21 15 50 25 20 50 32 8 50 52 2 50 75 12 50 116 2 50 129 12 50 165 17 50 199 26 50 227 28 50 256 3 50 300 11 50 340 6 50 396 0 50 404 0 51 2 14 51 11 9 51 18 4 51 27 0 51 47 26 51 73 1 51 99 10 51 132 1 51 166 31 51 199 0 51 222 9 51 259 21 51 292 20 51 334 24 51 411 0 51 419 0 52 15 21 52 16 27 52 28 7 52 37 11 52 67 22 52 97 13 52 149 14 52 175 30 52 187 6 52 218 18 52 271 10 52 282 26 52 347 15 52 426 0 52 434 0 53 4 20 53 20 19 53 31 15 53 38 9 53 70 0 53 103 28 53 122 2 53 162 7 53 180 2 53 213 19 53 252 5 53 320 19 53 354 9 53 441 0 53 449 0 54 3 7 54 8 0 54 24 15 54 34 5 54 60 2 54 94 0 54 113 9 54 156 20 54 182 0 54 216 11 54 284 28 54 288 31 54 348 18 54 456 0 54 464 0 55 0 11 55 24 28 55 37 8 55 47 26 55 61 3 55 89 22 55 121 23 55 156 10 55 191 3 55 214 7 55 242 3 55 278 0 55 327 25 55 471 0 55 479 0 56 2 9 56 11 24 56 23 6 56 26 6 56 35 20 56 55 3 56 83 20 56 113 10 56 142 28 56 178 22 56 205 11 56 237 1 56 273 22 56 313 4 56 352 19 56 367 0 56 375 0 57 2 21 57 14 11 57 19 23 57 32 1 57 51 1 57 73 17 57 107 21 57 142 22 57 173 5 57 197 12 57 229 15 57 262 22 57 300 28 57 354 8 57 382 0 57 390 0 58 15 13 58 22 15 58 26 20 58 33 8 58 53 2 58 76 12 58 117 2 58 130 12 58 166 17 58 192 27 58 228 28 58 257 3 58 301 11 58 341 6 58 397 0 58 405 0 59 3 14 59 12 9 59 19 4 59 28 0 59 40 27 59 74 1 59 100 10 59 133 1 59 167 31 59 192 1 59 223 9 59 260 21 59 293 20 59 335 24 59 412 0 59 420 0 60 8 22 60 17 27 60 29 7 60 38 11 60 68 22 60 98 13 60 150 14 60 168 31 60 188 6 60 219 18 60 264 11 60 283 26 60 348 15 60 427 0 60 435 0 61 5 20 61 21 19 61 24 16 61 39 9 61 71 0 61 96 29 61 123 2 61 163 7 61 181 2 61 214 19 61 253 5 61 321 19 61 355 9 61 442 0 61 450 0 62 4 7 62 9 0 62 25 15 62 35 5 62 61 2 62 95 0 62 114 9 62 157 20 62 183 0 62 217 11 62 285 28 62 289 31 62 349 18 62 457 0 62 465 0 63 1 18 63 16 6 63 30 27 63 34 23 63 63 0 63 94 6 63 126 11 63 155 23 63 177 29 63 212 23 63 251 16 63 315 30 63 320 2 63 362 0 63 472 0 64 2 13 64 13 11 64 16 26 64 38 5 64 71 13 64 85 5 64 106 22 64 136 25 64 175 31 64 205 21 64 234 1 64 269 1 64 308 3 64 346 14 64 368 0 64 376 0 65 3 21 65 15 11 65 20 23 65 33 1 65 52 1 65 74 17 65 108 21 65 143 22 65 174 5 65 198 12 65 230 15 65 263 22 65 301 28 65 355 8 65 383 0 65 391 0 66 8 14 66 23 15 66 27 20 66 34 8 66 54 2 66 77 12 66 118 2 66 131 12 66 167 17 66 193 27 66 229 28 66 258 3 66 302 11 66 342 6 66 398 0 66 406 0 67 4 14 67 13 9 67 20 4 67 29 0 67 41 27 67 75 1 67 101 10 67 134 1 67 160 0 67 193 1 67 216 10 67 261 21 67 294 20 67 328 25 67 413 0 67 421 0 68 9 22 68 18 27 68 30 7 68 39 11 68 69 22 68 99 13 68 151 14 68 169 31 68 189 6 68 220 18 68 265 11 68 284 26 68 349 15 68 428 0 68 436 0 69 6 20 69 22 19 69 25 16 69 32 10 69 64 1 69 97 29 69 124 2 69 164 7 69 182 2 69 215 19 69 254 5 69 322 19 69 356 9 69 443 0 69 451 0 70 5 7 70 10 0 70 26 15 70 36 5 70 62 2 70 88 1 70 115 9 70 158 20 70 176 1 70 218 11 70 286 28 70 290 31 70 350 18 70 458 0 70 466 0 71 2 18 71 17 6 71 31 27 71 35 23 71 56 1 71 95 6 71 127 11 71 156 23 71 178 29 71 213 23 71 252 16 71 316 30 71 321 2 71 363 0 71 473 0 72 3 13 72 14 11 72 17 26 72 39 5 72 64 14 72 86 5 72 107 22 72 137 25 72 168 0 72 206 21 72 235 1 72 270 1 72 309 3 72 347 14 72 369 0 72 377 0 73 4 3 73 14 9 73 16 21 73 37 18 73 50 14 73 86 6 73 112 4 73 128 28 73 172 12 73 191 12 73 225 4 73 274 1 73 310 3 73 339 1 73 384 0 73 392 0 74 9 14 74 16 16 74 28 20 74 35 8 74 55 2 74 78 12 74 119 2 74 132 12 74 160 18 74 194 27 74 230 28 74 259 3 74 303 11 74 343 6 74 399 0 74 407 0 75 5 14 75 14 9 75 21 4 75 30 0 75 42 27 75 76 1 75 102 10 75 135 1 75 161 0 75 194 1 75 217 10 75 262 21 75 295 20 75 329 25 75 414 0 75 422 0 76 10 22 76 19 27 76 31 7 76 32 12 76 70 22 76 100 13 76 144 15 76 170 31 76 190 6 76 221 18 76 266 11 76 285 26 76 350 15 76 429 0 76 437 0 77 7 20 77 23 19 77 26 16 77 33 10 77 65 1 77 98 29 77 125 2 77 165 7 77 183 2 77 208 20 77 255 5 77 323 19 77 357 9 77 444 0 77 452 0 78 6 7 78 11 0 78 27 15 78 37 5 78 63 2 78 89 1 78 116 9 78 159 20 78 177 1 78 219 11 78 287 28 78 291 31 78 351 18 78 459 0 78 467 0 79 3 18 79 18 6 79 24 28 79 36 23 79 57 1 79 88 7 79 120 12 79 157 23 79 179 29 79 214 23 79 253 16 79 317 30 79 322 2 79 364 0 79 474 0 80 4 13 80 15 11 80 18 26 80 32 6 80 65 14 80 87 5 80 108 22 80 138 25 80 169 0 80 207 21 80 236 1 80 271 1 80 310 3 80 348 14 80 370 0 80 378 0 81 5 3 81 15 9 81 17 21 81 38 18 81 51 14 81 87 6 81 113 4 81 129 28 81 173 12 81 184 13 81 226 4 81 275 1 81 311 3 81 340 1 81 385 0 81 393 0 82 11 2 82 23 21 82 29 4 82 45 31 82 81 10 82 110 6 82 142 3 82 162 31 82 200 2 82 237 25 82 301 4 82 306 12 82 340 0 82 400 0 82 408 0 83 6 14 83 15 9 83 22 4 83 31 0 83 43 27 83 77 1 83 103 10 83 128 2 83 162 0 83 195 1 83 218 10 83 263 21 83 288 21 83 330 25 83 415 0 83 423 0 84 11 22 84 20 27 84 24 8 84 33 12 84 71 22 84 101 13 84 145 15 84 171 31 84 191 6 84 222 18 84 267 11 84 286 26 84 351 15 84 430 0 84 438 0 85 0 21 85 16 20 85 27 16 85 34 10 85 66 1 85 99 29 85 126 2 85 166 7 85 176 3 85 209 20 85 248 6 85 324 19 85 358 9 85 445 0 85 453 0 86 7 7 86 12 0 86 28 15 86 38 5 86 56 3 86 90 1 86 117 9 86 152 21 86 178 1 86 220 11 86 280 29 86 292 31 86 344 19 86 460 0 86 468 0 87 4 18 87 19 6 87 25 28 87 37 23 87 58 1 87 89 7 87 121 12 87 158 23 87 180 29 87 215 23 87 254 16 87 318 30 87 323 2 87 365 0 87 475 0 88 5 13 88 8 12 88 19 26 88 33 6 88 66 14 88 80 6 88 109 22 88 139 25 88 170 0 88 200 22 88 237 1 88 264 2 88 311 3 88 349 14 88 371 0 88 379 0 89 6 3 89 8 10 89 18 21 89 39 18 89 52 14 89 80 7 89 114 4 89 130 28 89 174 12 89 185 13 89 227 4 89 276 1 89 304 4 89 341 1 89 386 0 89 394 0 90 12 2 90 16 22 90 30 4 90 46 31 90 82 10 90 111 6 90 143 3 90 163 31 90 201 2 90 238 25 90 302 4 90 307 12 90 341 0 90 401 0 90 409 0 91 3 25 91 9 1 91 18 8 91 29 9 91 45 1 91 74 11 91 103 2 91 151 0 91 152 28 91 205 26 91 247 13 91 253 10 91 319 14 91 361 0 91 416 0 91 424 0 92 12 22 92 21 27 92 25 8 92 34 12 92 64 23 92 102 13 92 146 15 92 172 31 92 184 7 92 223 18 92 268 11 92 287 26 92 344 16 92 431 0 92 439 0 93 1 21 93 17 20 93 28 16 93 35 10 93 67 1 93 100 29 93 127 2 93 167 7 93 177 3 93 210 20 93 249 6 93 325 19 93 359 9 93 446 0 93 454 0 94 0 8 94 13 0 94 29 15 94 39 5 94 57 3 94 91 1 94 118 9 94 153 21 94 179 1 94 221 11 94 281 29 94 293 31 94 345 19 94 461 0 94 469 0 95 5 18 95 20 6 95 26 28 95 38 23 95 59 1 95 90 7 95 122 12 95 159 23 95 181 29 95 208 24 95 255 16 95 319 30 95 324 2 95 366 0 95 476 0 96 6 13 96 9 12 96 20 26 96 34 6 96 67 14 96 81 6 96 110 22 96 140 25 96 171 0 96 201 22 96 238 1 96 265 2 96 304 4 96 350 14 96 372 0 96 380 0 97 7 3 97 9 10 97 19 21 97 32 19 97 53 14 97 81 7 97 115 4 97 131 28 97 175 12 97 186 13 97 228 4 97 277 1 97 305 4 97 342 1 97 387 0 97 395 0 98 13 2 98 17 22 98 31 4 98 47 31 98 83 10 98 104 7 98 136 4 98 164 31 98 202 2 98 239 25 98 303 4 98 308 12 98 342 0 98 402 0 98 410 0 99 4 25 99 10 1 99 19 8 99 30 9 99 46 1 99 75 11 99 96 3 99 144 1 99 153 28 99 206 26 99 240 14 99 254 10 99 312 15 99 362 0 99 417 0 99 425 0 100 1 27 100 9 27 100 18 30 100 27 28 100 33 11 100 71 2 100 104 10 100 124 8 100 147 26 100 190 18 100 218 4 100 265 1 100 282 7 100 333 3 100 432 0 100 440 0 101 2 21 101 18 20 101 29 16 101 36 10 101 68 1 101 101 29 101 120 3 101 160 8 101 178 3 101 211 20 101 250 6 101 326 19 101 352 10 101 447 0 101 455 0 102 1 8 102 14 0 102 30 15 102 32 6 102 58 3 102 92 1 102 119 9 102 154 21 102 180 1 102 222 11 102 282 29 102 294 31 102 346 19 102 462 0 102 470 0 103 6 18 103 21 6 103 27 28 103 39 23 103 60 1 103 91 7 103 123 12 103 152 24 103 182 29 103 209 24 103 248 17 103 312 31 103 325 2 103 367 0 103 477 0 104 7 13 104 10 12 104 21 26 104 35 6 104 68 14 104 82 6 104 111 22 104 141 25 104 172 0 104 202 22 104 239 1 104 266 2 104 305 4 104 351 14 104 373 0 104 381 0 105 0 4 105 10 10 105 20 21 105 33 19 105 54 14 105 82 7 105 116 4 105 132 28 105 168 13 105 187 13 105 229 4 105 278 1 105 306 4 105 343 1 105 388 0 105 396 0 106 14 2 106 18 22 106 24 5 106 40 0 106 84 10 106 105 7 106 137 4 106 165 31 106 203 2 106 232 26 106 296 5 106 309 12 106 343 0 106 403 0 106 411 0 107 5 25 107 11 1 107 20 8 107 31 9 107 47 1 107 76 11 107 97 3 107 145 1 107 154 28 107 207 26 107 241 14 107 255 10 107 313 15 107 363 0 107 418 0 107 426 0 108 2 27 108 10 27 108 19 30 108 28 28 108 34 11 108 64 3 108 105 10 108 125 8 108 148 26 108 191 18 108 219 4 108 266 1 108 283 7 108 334 3 108 433 0 108 441 0 109 7 23 109 15 21 109 27 20 109 39 2 109 58 29 109 95 28 109 130 10 109 146 13 109 198 20 109 215 30 109 246 27 109 294 24 109 332 2 109 448 0 109 456 0 110 2 8 110 15 0 110 31 15 110 33 6 110 59 3 110 93 1 110 112 10 110 155 21 110 181 1 110 223 11 110 283 29 110 295 31 110 347 19 110 463 0 110 471 0 111 7 18 111 22 6 111 28 28 111 32 24 111 61 1 111 92 7 111 124 12 111 153 24 111 183 29 111 210 24 111 249 17 111 313 31 111 326 2 111 360 1 111 478 0 112 0 14 112 11 12 112 22 26 112 36 6 112 69 14 112 83 6 112 104 23 112 142 25 112 173 0 112 203 22 112 232 2 112 267 2 112 306 4 112 344 15 112 374 0 112 382 0 113 1 4 113 11 10 113 21 21 113 34 19 113 55 14 113 83 7 113 117 4 113 133 28 113 169 13 113 188 13 113 230 4 113 279 1 113 307 4 113 336 2 113 389 0 113 397 0 114 15 2 114 19 22 114 25 5 114 41 0 114 85 10 114 106 7 114 138 4 114 166 31 114 204 2 114 233 26 114 297 5 114 310 12 114 336 1 114 404 0 114 412 0 115 6 25 115 12 1 115 21 8 115 24 10 115 40 2 115 77 11 115 98 3 115 146 1 115 155 28 115 200 27 115 242 14 115 248 11 115 314 15 115 364 0 115 419 0 115 427 0 116 3 27 116 11 27 116 20 30 116 29 28 116 35 11 116 65 3 116 106 10 116 126 8 116 149 26 116 184 19 116 220 4 116 267 1 116 284 7 116 335 3 116 434 0 116 442 0 117 0 24 117 8 22 117 28 20 117 32 3 117 59 29 117 88 29 117 131 10 117 147 13 117 199 20 117 208 31 117 247 27 117 295 24 117 333 2 117 449 0 117 457 0 118 1 10 118 25 27 118 38 7 118 40 26 118 62 2 118 90 21 118 122 22 118 157 9 118 184 3 118 215 6 118 243 2 118 279 31 118 320 25 118 464 0 118 472 0 119 0 19 119 23 6 119 29 28 119 33 24 119 62 1 119 93 7 119 125 12 119 154 24 119 176 30 119 211 24 119 250 17 119 314 31 119 327 2 119 361 1 119 479 0

APPENDIX TABLE G Specification of the base matrix B_(4/5) for the rate-⅘ LDPC code 0 6 27 0 9 9 0 20 10 0 29 13 0 33 11 0 53 26 0 58 28 0 76 2 0 102 0 0 121 0 0 145 0 0 171 0 0 189 30 0 226 16 0 254 20 0 282 25 0 325 1 0 351 20 0 380 10 0 384 0 0 392 0 1 3 23 1 14 5 1 20 20 1 25 8 1 33 24 1 44 5 1 77 5 1 102 3 1 123 1 1 148 1 1 188 15 1 196 7 1 219 7 1 252 1 1 281 5 1 312 24 1 345 23 1 374 21 1 396 0 1 404 0 2 2 19 2 11 8 2 21 13 2 30 6 2 34 9 2 72 31 2 88 0 2 112 0 2 136 0 2 167 10 2 188 19 2 223 15 2 247 19 2 280 17 2 319 0 2 339 9 2 371 11 2 408 0 2 416 0 3 7 19 3 13 5 3 16 23 3 31 7 3 34 24 3 41 3 3 69 3 3 88 1 3 124 17 3 142 0 3 164 13 3 180 13 3 214 9 3 256 9 3 279 28 3 307 1 3 334 9 3 361 29 3 420 0 3 428 0 4 3 0 4 9 0 4 21 0 4 29 1 4 33 9 4 58 3 4 86 2 4 107 10 4 131 5 4 161 8 4 177 7 4 206 17 4 233 13 4 267 13 4 300 8 4 355 5 4 385 0 4 432 0 4 440 0 5 0 1 5 10 1 5 16 20 5 25 20 5 34 13 5 69 27 5 97 19 5 114 10 5 141 5 5 155 10 5 179 28 5 205 0 5 233 11 5 270 30 5 300 5 5 323 13 5 354 23 5 444 0 5 452 0 6 0 0 6 15 1 6 23 29 6 29 17 6 37 9 6 53 31 6 83 13 6 104 22 6 130 4 6 154 1 6 193 8 6 213 25 6 224 18 6 279 3 6 290 29 6 334 4 6 362 4 6 456 0 6 464 0 7 1 8 7 13 6 7 19 18 7 26 26 7 33 4 7 49 3 7 76 25 7 103 0 7 128 8 7 148 8 7 168 6 7 192 22 7 245 2 7 257 7 7 293 1 7 337 28 7 363 2 7 468 0 7 476 0 8 7 27 8 10 9 8 21 10 8 30 13 8 34 11 8 54 26 8 59 28 8 77 2 8 103 0 8 122 0 8 146 0 8 172 0 8 190 30 8 227 16 8 255 20 8 283 25 8 326 1 8 344 21 8 381 10 8 385 0 8 393 0 9 4 23 9 15 5 9 21 20 9 26 8 9 34 24 9 45 5 9 78 5 9 103 3 9 124 1 9 149 1 9 189 15 9 197 7 9 220 7 9 253 1 9 282 5 9 313 24 9 346 23 9 375 21 9 397 0 9 405 0 10 3 19 10 12 8 10 22 13 10 31 6 10 35 9 10 73 31 10 89 0 10 113 0 10 137 0 10 160 11 10 189 19 10 216 16 10 240 20 10 281 17 10 312 1 10 340 9 10 372 11 10 409 0 10 417 0 11 0 20 11 14 5 11 17 23 11 24 8 11 35 24 11 42 3 11 70 3 11 89 1 11 125 17 11 143 0 11 165 13 11 181 13 11 215 9 11 257 9 11 272 29 11 308 1 11 335 9 11 362 29 11 421 0 11 429 0 12 4 0 12 10 0 12 22 0 12 30 1 12 34 9 12 59 3 12 87 2 12 108 10 12 132 5 12 162 8 12 178 7 12 207 17 12 234 13 12 268 13 12 301 8 12 356 5 12 386 0 12 433 0 12 441 0 13 1 1 13 11 1 13 17 20 13 26 20 13 35 13 13 70 27 13 98 19 13 115 10 13 142 5 13 156 10 13 180 28 13 206 0 13 234 11 13 271 30 13 301 5 13 324 13 13 355 23 13 445 0 13 453 0 14 1 0 14 8 2 14 16 30 14 30 17 14 38 9 14 54 31 14 84 13 14 105 22 14 131 4 14 155 1 14 194 8 14 214 25 14 225 18 14 272 4 14 291 29 14 335 4 14 363 4 14 457 0 14 465 0 15 2 8 15 14 6 15 20 18 15 27 26 15 34 4 15 50 3 15 77 25 15 96 1 15 129 8 15 149 8 15 169 6 15 193 22 15 246 2 15 258 7 15 294 1 15 338 28 15 364 2 15 469 0 15 477 0 16 0 28 16 11 9 16 22 10 16 31 13 16 35 11 16 55 26 16 60 28 16 78 2 16 96 1 16 123 0 16 147 0 16 173 0 16 191 30 16 228 16 16 248 21 16 284 25 16 327 1 16 345 21 16 382 10 16 386 0 16 394 0 17 5 23 17 8 6 17 22 20 17 27 8 17 35 24 17 46 5 17 79 5 17 96 4 17 125 1 17 150 1 17 190 15 17 198 7 17 221 7 17 254 1 17 283 5 17 314 24 17 347 23 17 368 22 17 398 0 17 406 0 18 4 19 18 13 8 18 23 13 18 24 7 18 36 9 18 74 31 18 90 0 18 114 0 18 138 0 18 161 11 18 190 19 18 217 16 18 241 20 18 282 17 18 313 1 18 341 9 18 373 11 18 410 0 18 418 0 19 1 20 19 15 5 19 18 23 19 25 8 19 36 24 19 43 3 19 71 3 19 90 1 19 126 17 19 136 1 19 166 13 19 182 13 19 208 10 19 258 9 19 273 29 19 309 1 19 328 10 19 363 29 19 422 0 19 430 0 20 5 0 20 11 0 20 23 0 20 31 1 20 35 9 20 60 3 20 80 3 20 109 10 20 133 5 20 163 8 20 179 7 20 200 18 20 235 13 20 269 13 20 302 8 20 357 5 20 387 0 20 434 0 20 442 0 21 2 1 21 12 1 21 18 20 21 27 20 21 36 13 21 71 27 21 99 19 21 116 10 21 143 5 21 157 10 21 181 28 21 207 0 21 235 11 21 264 31 21 302 5 21 325 13 21 356 23 21 446 0 21 454 0 22 2 0 22 9 2 22 17 30 22 31 17 22 39 9 22 55 31 22 85 13 22 106 22 22 132 4 22 156 1 22 195 8 22 215 25 22 226 18 22 273 4 22 292 29 22 328 5 22 364 4 22 458 0 22 466 0 23 3 8 23 15 6 23 21 18 23 28 26 23 35 4 23 51 3 23 78 25 23 97 1 23 130 8 23 150 8 23 170 6 23 194 22 23 247 2 23 259 7 23 295 1 23 339 28 23 365 2 23 470 0 23 478 0 24 1 28 24 12 9 24 23 10 24 24 14 24 36 11 24 48 27 24 61 28 24 79 2 24 97 1 24 124 0 24 148 0 24 174 0 24 184 31 24 229 16 24 249 21 24 285 25 24 320 2 24 346 21 24 383 10 24 387 0 24 395 0 25 6 23 25 9 6 25 23 20 25 28 8 25 36 24 25 47 5 25 72 6 25 97 4 25 126 1 25 151 1 25 191 15 25 199 7 25 222 7 25 255 1 25 284 5 25 315 24 25 348 23 25 369 22 25 399 0 25 407 0 26 5 19 26 14 8 26 16 14 26 25 7 26 37 9 26 75 31 26 91 0 26 115 0 26 139 0 26 162 11 26 191 19 26 218 16 26 242 20 26 283 17 26 314 1 26 342 9 26 374 11 26 411 0 26 419 0 27 2 20 27 8 6 27 19 23 27 26 8 27 37 24 27 44 3 27 64 4 27 91 1 27 127 17 27 137 1 27 167 13 27 183 13 27 209 10 27 259 9 27 274 29 27 310 1 27 329 10 27 364 29 27 423 0 27 431 0 28 6 0 28 12 0 28 16 1 28 24 2 28 36 9 28 61 3 28 81 3 28 110 10 28 134 5 28 164 8 28 180 7 28 201 18 28 236 13 28 270 13 28 303 8 28 358 5 28 388 0 28 435 0 28 443 0 29 3 1 29 13 1 29 19 20 29 28 20 29 37 13 29 64 28 29 100 19 29 117 10 29 136 6 29 158 10 29 182 28 29 200 1 29 236 11 29 265 31 29 303 5 29 326 13 29 357 23 29 447 0 29 455 0 30 3 0 30 10 2 30 18 30 30 24 18 30 32 10 30 48 0 30 86 13 30 107 22 30 133 4 30 157 1 30 196 8 30 208 26 30 227 18 30 274 4 30 293 29 30 329 5 30 365 4 30 459 0 30 467 0 31 4 8 31 8 7 31 22 18 31 29 26 31 36 4 31 52 3 31 79 25 31 98 1 31 131 8 31 151 8 31 171 6 31 195 22 31 240 3 31 260 7 31 288 2 31 340 28 31 366 2 31 471 0 31 479 0 32 2 28 32 13 9 32 16 11 32 25 14 32 37 11 32 49 27 32 62 28 32 72 3 32 98 1 32 125 0 32 149 0 32 175 0 32 185 31 32 230 16 32 250 21 32 286 25 32 321 2 32 347 21 32 376 11 32 388 0 32 396 0 33 2 28 33 14 12 33 22 0 33 31 18 33 35 6 33 40 1 33 70 28 33 94 17 33 118 26 33 140 29 33 171 5 33 188 29 33 217 0 33 251 9 33 273 21 33 319 11 33 341 14 33 383 31 33 400 0 33 408 0 34 6 19 34 15 8 34 17 14 34 26 7 34 38 9 34 76 31 34 92 0 34 116 0 34 140 0 34 163 11 34 184 20 34 219 16 34 243 20 34 284 17 34 315 1 34 343 9 34 375 11 34 412 0 34 420 0 35 2 7 35 13 29 35 16 30 35 30 21 35 35 2 35 50 10 35 57 26 35 92 6 35 116 4 35 152 6 35 162 0 35 178 6 35 209 1 35 244 1 35 265 28 35 304 13 35 347 29 35 373 2 35 424 0 35 432 0 36 7 0 36 13 0 36 17 1 36 25 2 36 37 9 36 62 3 36 82 3 36 111 10 36 135 5 36 165 8 36 181 7 36 202 18 36 237 13 36 271 13 36 296 9 36 359 5 36 389 0 36 436 0 36 444 0 37 4 9 37 11 1 37 19 0 37 30 7 37 38 5 37 65 15 37 81 1 37 106 0 37 128 0 37 152 2 37 194 7 37 200 9 37 236 21 37 258 9 37 306 24 37 333 8 37 380 1 37 448 0 37 456 0 38 4 0 38 11 2 38 19 30 38 25 18 38 33 10 38 49 0 38 87 13 38 108 22 38 134 4 38 158 1 38 197 8 38 209 26 38 228 18 38 275 4 38 294 29 38 330 5 38 366 4 38 460 0 38 468 0 39 5 8 39 13 28 39 18 21 39 25 24 39 34 16 39 47 19 39 57 14 39 81 20 39 110 13 39 127 24 39 144 0 39 169 20 39 200 22 39 225 1 39 294 30 39 297 4 39 320 2 39 354 1 39 386 0 39 472 0 40 3 28 40 14 9 40 17 11 40 26 14 40 38 11 40 50 27 40 63 28 40 73 3 40 99 1 40 126 0 40 150 0 40 168 1 40 186 31 40 231 16 40 251 21 40 287 25 40 322 2 40 348 21 40 377 11 40 389 0 40 397 0 41 3 28 41 15 12 41 23 0 41 24 19 41 36 6 41 41 1 41 71 28 41 95 17 41 119 26 41 141 29 41 172 5 41 189 29 41 218 0 41 252 9 41 274 21 41 312 12 41 342 14 41 376 0 41 401 0 41 409 0 42 7 19 42 8 9 42 18 14 42 27 7 42 39 9 42 77 31 42 93 0 42 117 0 42 141 0 42 164 11 42 185 20 42 220 16 42 244 20 42 285 17 42 316 1 42 336 10 42 368 12 42 413 0 42 421 0 43 3 7 43 14 29 43 17 30 43 31 21 43 36 2 43 51 10 43 58 26 43 93 6 43 117 4 43 153 6 43 163 0 43 179 6 43 210 1 43 245 1 43 266 28 43 305 13 43 348 29 43 374 2 43 425 0 43 433 0 44 0 1 44 14 0 44 18 1 44 26 2 44 38 9 44 63 3 44 83 3 44 104 11 44 128 6 44 166 8 44 182 7 44 203 18 44 238 13 44 264 14 44 297 9 44 352 6 44 390 0 44 437 0 44 445 0 45 5 9 45 12 1 45 20 0 45 31 7 45 39 5 45 66 15 45 82 1 45 107 0 45 129 0 45 153 2 45 195 7 45 201 9 45 237 21 45 259 9 45 307 24 45 334 8 45 381 1 45 449 0 45 457 0 46 5 0 46 12 2 46 20 30 46 26 18 46 34 10 46 50 0 46 80 14 46 109 22 46 135 4 46 159 1 46 198 8 46 210 26 46 229 18 46 276 4 46 295 29 46 331 5 46 367 4 46 461 0 46 469 0 47 6 8 47 14 28 47 19 21 47 26 24 47 35 16 47 40 20 47 58 14 47 82 20 47 111 13 47 120 25 47 145 0 47 170 20 47 201 22 47 226 1 47 295 30 47 298 4 47 321 2 47 355 1 47 387 0 47 473 0 48 4 28 48 15 9 48 18 11 48 27 14 48 39 11 48 51 27 48 56 29 48 74 3 48 100 1 48 127 0 48 151 0 48 169 1 48 187 31 48 224 17 48 252 21 48 280 26 48 323 2 48 349 21 48 378 11 48 390 0 48 398 0 49 4 28 49 8 13 49 16 1 49 25 19 49 37 6 49 42 1 49 64 29 49 88 18 49 112 27 49 142 29 49 173 5 49 190 29 49 219 0 49 253 9 49 275 21 49 313 12 49 343 14 49 377 0 49 402 0 49 410 0 50 0 20 50 9 9 50 19 14 50 28 7 50 32 10 50 78 31 50 94 0 50 118 0 50 142 0 50 165 11 50 186 20 50 221 16 50 245 20 50 286 17 50 317 1 50 337 10 50 369 12 50 414 0 50 422 0 51 4 7 51 15 29 51 18 30 51 24 22 51 37 2 51 52 10 51 59 26 51 94 6 51 118 4 51 154 6 51 164 0 51 180 6 51 211 1 51 246 1 51 267 28 51 306 13 51 349 29 51 375 2 51 426 0 51 434 0 52 1 1 52 15 0 52 19 1 52 27 2 52 39 9 52 56 4 52 84 3 52 105 11 52 129 6 52 167 8 52 183 7 52 204 18 52 239 13 52 265 14 52 298 9 52 353 6 52 391 0 52 438 0 52 446 0 53 6 9 53 13 1 53 21 0 53 24 8 53 32 6 53 67 15 53 83 1 53 108 0 53 130 0 53 154 2 53 196 7 53 202 9 53 238 21 53 260 9 53 308 24 53 335 8 53 382 1 53 450 0 53 458 0 54 6 0 54 13 2 54 21 30 54 27 18 54 35 10 54 51 0 54 81 14 54 110 22 54 128 5 54 152 2 54 199 8 54 211 26 54 230 18 54 277 4 54 288 30 54 332 5 54 360 5 54 462 0 54 470 0 55 7 8 55 15 28 55 20 21 55 27 24 55 36 16 55 41 20 55 59 14 55 83 20 55 104 14 55 121 25 55 146 0 55 171 20 55 202 22 55 227 1 55 288 31 55 299 4 55 322 2 55 356 1 55 388 0 55 474 0 56 5 28 56 8 10 56 19 11 56 28 14 56 32 12 56 52 27 56 57 29 56 75 3 56 101 1 56 120 1 56 144 1 56 170 1 56 188 31 56 225 17 56 253 21 56 281 26 56 324 2 56 350 21 56 379 11 56 391 0 56 399 0 57 5 28 57 9 13 57 17 1 57 26 19 57 38 6 57 43 1 57 65 29 57 89 18 57 113 27 57 143 29 57 174 5 57 191 29 57 220 0 57 254 9 57 276 21 57 314 12 57 336 15 57 378 0 57 403 0 57 411 0 58 1 20 58 10 9 58 20 14 58 29 7 58 33 10 58 79 31 58 95 0 58 119 0 58 143 0 58 166 11 58 187 20 58 222 16 58 246 20 58 287 17 58 318 1 58 338 10 58 370 12 58 415 0 58 423 0 59 5 7 59 8 30 59 19 30 59 25 22 59 38 2 59 53 10 59 60 26 59 95 6 59 119 4 59 155 6 59 165 0 59 181 6 59 212 1 59 247 1 59 268 28 59 307 13 59 350 29 59 368 3 59 427 0 59 435 0 60 2 1 60 8 1 60 20 1 60 28 2 60 32 10 60 57 4 60 85 3 60 106 11 60 130 6 60 160 9 60 176 8 60 205 18 60 232 14 60 266 14 60 299 9 60 354 6 60 384 1 60 439 0 60 447 0 61 7 9 61 14 1 61 22 0 61 25 8 61 33 6 61 68 15 61 84 1 61 109 0 61 131 0 61 155 2 61 197 7 61 203 9 61 239 21 61 261 9 61 309 24 61 328 9 61 383 1 61 451 0 61 459 0 62 7 0 62 14 2 62 22 30 62 28 18 62 36 10 62 52 0 62 82 14 62 111 22 62 129 5 62 153 2 62 192 9 62 212 26 62 231 18 62 278 4 62 289 30 62 333 5 62 361 5 62 463 0 62 471 0 63 0 9 63 8 29 63 21 21 63 28 24 63 37 16 63 42 20 63 60 14 63 84 20 63 105 14 63 122 25 63 147 0 63 172 20 63 203 22 63 228 1 63 289 31 63 300 4 63 323 2 63 357 1 63 389 0 63 475 0 64 7 22 64 10 5 64 16 20 64 29 7 64 37 23 64 40 5 64 73 5 64 98 3 64 127 0 64 144 1 64 184 15 64 192 7 64 223 6 64 248 1 64 285 4 64 316 23 64 349 22 64 370 21 64 392 0 64 400 0 65 6 28 65 10 13 65 18 1 65 27 19 65 39 6 65 44 1 65 66 29 65 90 18 65 114 27 65 136 30 65 175 5 65 184 30 65 221 0 65 255 9 65 277 21 65 315 12 65 337 15 65 379 0 65 404 0 65 412 0 66 3 19 66 9 5 66 20 22 66 27 7 66 38 23 66 45 2 66 65 3 66 92 0 66 120 17 66 138 0 66 160 13 66 176 13 66 210 9 66 260 8 66 275 28 66 311 0 66 330 9 66 365 28 66 416 0 66 424 0 67 6 7 67 9 30 67 20 30 67 26 22 67 39 2 67 54 10 67 61 26 67 88 7 67 112 5 67 156 6 67 166 0 67 182 6 67 213 1 67 240 2 67 269 28 67 308 13 67 351 29 67 369 3 67 428 0 67 436 0 68 4 0 68 14 0 68 20 19 68 29 19 68 38 12 68 65 27 68 101 18 68 118 9 68 137 5 68 159 9 68 183 27 68 201 0 68 237 10 68 266 30 68 296 5 68 327 12 68 358 22 68 440 0 68 448 0 69 0 10 69 15 1 69 23 0 69 26 8 69 34 6 69 69 15 69 85 1 69 110 0 69 132 0 69 156 2 69 198 7 69 204 9 69 232 22 69 262 9 69 310 24 69 329 9 69 376 2 69 452 0 69 460 0 70 5 7 70 9 6 70 23 17 70 30 25 70 37 3 70 53 2 70 72 25 70 99 0 70 132 7 70 144 8 70 172 5 70 196 21 70 241 2 70 261 6 70 289 1 70 341 27 70 367 1 70 464 0 70 472 0 71 1 9 71 9 29 71 22 21 71 29 24 71 38 16 71 43 20 71 61 14 71 85 20 71 106 14 71 123 25 71 148 0 71 173 20 71 204 22 71 229 1 71 290 31 71 301 4 71 324 2 71 358 1 71 390 0 71 476 0 72 0 23 72 11 5 72 17 20 72 30 7 72 38 23 72 41 5 72 74 5 72 99 3 72 120 1 72 145 1 72 185 15 72 193 7 72 216 7 72 249 1 72 286 4 72 317 23 72 350 22 72 371 21 72 393 0 72 401 0 73 7 28 73 11 13 73 19 1 73 28 19 73 32 7 73 45 1 73 67 29 73 91 18 73 115 27 73 137 30 73 168 6 73 185 30 73 222 0 73 248 10 73 278 21 73 316 12 73 338 15 73 380 0 73 405 0 73 413 0 74 4 19 74 10 5 74 21 22 74 28 7 74 39 23 74 46 2 74 66 3 74 93 0 74 121 17 74 139 0 74 161 13 74 177 13 74 211 9 74 261 8 74 276 28 74 304 1 74 331 9 74 366 28 74 417 0 74 425 0 75 7 7 75 10 30 75 21 30 75 27 22 75 32 3 75 55 10 75 62 26 75 89 7 75 113 5 75 157 6 75 167 0 75 183 6 75 214 1 75 241 2 75 270 28 75 309 13 75 344 30 75 370 3 75 429 0 75 437 0 76 5 0 76 15 0 76 21 19 76 30 19 76 39 12 76 66 27 76 102 18 76 119 9 76 138 5 76 152 10 76 176 28 76 202 0 76 238 10 76 267 30 76 297 5 76 320 13 76 359 22 76 441 0 76 449 0 77 1 10 77 8 2 77 16 1 77 27 8 77 35 6 77 70 15 77 86 1 77 111 0 77 133 0 77 157 2 77 199 7 77 205 9 77 233 22 77 263 9 77 311 24 77 330 9 77 377 2 77 453 0 77 461 0 78 6 7 78 10 6 78 16 18 78 31 25 78 38 3 78 54 2 78 73 25 78 100 0 78 133 7 78 145 8 78 173 5 78 197 21 78 242 2 78 262 6 78 290 1 78 342 27 78 360 2 78 465 0 78 473 0 79 2 9 79 10 29 79 23 21 79 30 24 79 39 16 79 44 20 79 62 14 79 86 20 79 107 14 79 124 25 79 149 0 79 174 20 79 205 22 79 230 1 79 291 31 79 302 4 79 325 2 79 359 1 79 391 0 79 477 0 80 1 23 80 12 5 80 18 20 80 31 7 80 39 23 80 42 5 80 75 5 80 100 3 80 121 1 80 146 1 80 186 15 80 194 7 80 217 7 80 250 1 80 287 4 80 318 23 80 351 22 80 372 21 80 394 0 80 402 0 81 0 29 81 12 13 81 20 1 81 29 19 81 33 7 81 46 1 81 68 29 81 92 18 81 116 27 81 138 30 81 169 6 81 186 30 81 223 0 81 249 10 81 279 21 81 317 12 81 339 15 81 381 0 81 406 0 81 414 0 82 5 19 82 11 5 82 22 22 82 29 7 82 32 24 82 47 2 82 67 3 82 94 0 82 122 17 82 140 0 82 162 13 82 178 13 82 212 9 82 262 8 82 277 28 82 305 1 82 332 9 82 367 28 82 418 0 82 426 0 83 0 8 83 11 30 83 22 30 83 28 22 83 33 3 83 48 11 83 63 26 83 90 7 83 114 5 83 158 6 83 160 1 83 176 7 83 215 1 83 242 2 83 271 28 83 310 13 83 345 30 83 371 3 83 430 0 83 438 0 84 6 0 84 8 1 84 22 19 84 31 19 84 32 13 84 67 27 84 103 18 84 112 10 84 139 5 84 153 10 84 177 28 84 203 0 84 239 10 84 268 30 84 298 5 84 321 13 84 352 23 84 442 0 84 450 0 85 2 10 85 9 2 85 17 1 85 28 8 85 36 6 85 71 15 85 87 1 85 104 1 85 134 0 85 158 2 85 192 8 85 206 9 85 234 22 85 256 10 85 304 25 85 331 9 85 378 2 85 454 0 85 462 0 86 7 7 86 11 6 86 17 18 86 24 26 86 39 3 86 55 2 86 74 25 86 101 0 86 134 7 86 146 8 86 174 5 86 198 21 86 243 2 86 263 6 86 291 1 86 343 27 86 361 2 86 466 0 86 474 0 87 3 9 87 11 29 87 16 22 87 31 24 87 32 17 87 45 20 87 63 14 87 87 20 87 108 14 87 125 25 87 150 0 87 175 20 87 206 22 87 231 1 87 292 31 87 303 4 87 326 2 87 352 2 87 384 1 87 478 0 88 2 23 88 13 5 88 19 20 88 24 8 88 32 24 88 43 5 88 76 5 88 101 3 88 122 1 88 147 1 88 187 15 88 195 7 88 218 7 88 251 1 88 280 5 88 319 23 88 344 23 88 373 21 88 395 0 88 403 0 89 1 29 89 13 13 89 21 1 89 30 19 89 34 7 89 47 1 89 69 29 89 93 18 89 117 27 89 139 30 89 170 6 89 187 30 89 216 1 89 250 10 89 272 22 89 318 12 89 340 15 89 382 0 89 407 0 89 415 0 90 6 19 90 12 5 90 23 22 90 30 7 90 33 24 90 40 3 90 68 3 90 95 0 90 123 17 90 141 0 90 163 13 90 179 13 90 213 9 90 263 8 90 278 28 90 306 1 90 333 9 90 360 29 90 419 0 90 427 0 91 1 8 91 12 30 91 23 30 91 29 22 91 34 3 91 49 11 91 56 27 91 91 7 91 115 5 91 159 6 91 161 1 91 177 7 91 208 2 91 243 2 91 264 29 91 311 13 91 346 30 91 372 3 91 431 0 91 439 0 92 7 0 92 9 1 92 23 19 92 24 20 92 33 13 92 68 27 92 96 19 92 113 10 92 140 5 92 154 10 92 178 28 92 204 0 92 232 11 92 269 30 92 299 5 92 322 13 92 353 23 92 443 0 92 451 0 93 3 10 93 10 2 93 18 1 93 29 8 93 37 6 93 64 16 93 80 2 93 105 1 93 135 0 93 159 2 93 193 8 93 207 9 93 235 22 93 257 10 93 305 25 93 332 9 93 379 2 93 455 0 93 463 0 94 0 8 94 12 6 94 18 18 94 25 26 94 32 4 94 48 3 94 75 25 94 102 0 94 135 7 94 147 8 94 175 5 94 199 21 94 244 2 94 256 7 94 292 1 94 336 28 94 362 2 94 467 0 94 475 0 95 4 9 95 12 29 95 17 22 95 24 25 95 33 17 95 46 20 95 56 15 95 80 21 95 109 14 95 126 25 95 151 0 95 168 21 95 207 22 95 224 2 95 293 31 95 296 5 95 327 2 95 353 2 95 385 1 95 479 0

APPENDIX TABLE H Specification of the base matrix B_(5/6) for the rate-⅚ LDPC code 0 7 16 0 15 20 0 19 28 0 26 11 0 35 1 0 40 16 0 56 31 0 74 18 0 88 12 0 105 5 0 126 18 0 144 27 0 163 1 0 187 6 0 202 0 0 230 0 0 241 13 0 266 10 0 293 31 0 326 6 0 349 1 0 368 7 0 399 18 0 400 0 0 408 0 1 4 1 1 11 0 1 17 1 1 25 1 1 36 16 1 40 24 1 58 17 1 76 14 1 107 28 1 126 1 1 139 1 1 162 3 1 177 28 1 202 2 1 229 3 1 240 22 1 259 6 1 295 7 1 316 10 1 339 30 1 373 22 1 396 8 1 410 0 1 418 0 2 0 15 2 15 30 2 23 11 2 26 0 2 32 8 2 46 15 2 49 4 2 75 18 2 86 22 2 100 22 2 117 13 2 141 9 2 153 27 2 182 1 2 194 17 2 216 16 2 245 15 2 262 3 2 282 1 2 315 1 2 348 12 2 360 15 2 389 20 2 420 0 2 428 0 3 2 10 3 13 3 3 20 4 3 30 24 3 38 0 3 44 6 3 52 31 3 79 23 3 100 10 3 119 18 3 157 2 3 164 1 3 183 1 3 204 7 3 218 2 3 242 28 3 256 15 3 282 22 3 306 11 3 343 4 3 363 20 3 387 0 3 430 0 3 438 0 4 4 21 4 10 1 4 23 22 4 30 24 4 34 27 4 41 15 4 55 31 4 65 0 4 91 15 4 114 31 4 149 17 4 155 2 4 187 6 4 197 1 4 210 16 4 233 14 4 251 10 4 274 7 4 300 30 4 332 29 4 355 27 4 401 0 4 440 0 4 448 0 5 0 1 5 8 27 5 16 5 5 29 30 5 36 30 5 45 11 5 65 1 5 90 0 5 118 25 5 134 23 5 151 10 5 172 0 5 187 4 5 211 9 5 238 10 5 251 1 5 265 25 5 301 4 5 330 11 5 357 16 5 380 11 5 450 0 5 458 0 6 5 20 6 13 25 6 20 11 6 31 8 6 35 17 6 44 5 6 71 15 6 80 26 6 90 11 6 106 13 6 124 0 6 146 1 6 163 12 6 199 3 6 202 23 6 233 3 6 249 18 6 308 29 6 314 11 6 322 1 6 373 15 6 395 10 6 460 0 6 468 0 7 3 1 7 8 1 7 18 1 7 30 0 7 37 8 7 44 3 7 63 4 7 80 10 7 110 4 7 134 20 7 140 10 7 175 23 7 186 1 7 213 31 7 225 13 7 248 0 7 278 21 7 299 2 7 328 1 7 352 15 7 377 5 7 470 0 7 478 0 8 0 17 8 8 21 8 20 28 8 27 11 8 36 1 8 41 16 8 57 31 8 75 18 8 89 12 8 106 5 8 127 18 8 145 27 8 164 1 8 188 6 8 203 0 8 231 0 8 242 13 8 267 10 8 294 31 8 327 6 8 350 1 8 369 7 8 392 19 8 401 0 8 409 0 9 5 1 9 12 0 9 18 1 9 26 1 9 37 16 9 41 24 9 59 17 9 77 14 9 108 28 9 127 1 9 140 1 9 163 3 9 178 28 9 203 2 9 230 3 9 241 22 9 260 6 9 288 8 9 317 10 9 340 30 9 374 22 9 397 8 9 411 0 9 419 0 10 1 15 10 8 31 10 16 12 10 27 0 10 33 8 10 47 15 10 50 4 10 76 18 10 87 22 10 101 22 10 118 13 10 142 9 10 154 27 10 183 1 10 195 17 10 217 16 10 246 15 10 263 3 10 283 1 10 316 1 10 349 12 10 361 15 10 390 20 10 421 0 10 429 0 11 3 10 11 14 3 11 21 4 11 31 24 11 39 0 11 45 6 11 53 31 11 72 24 11 101 10 11 112 19 11 158 2 11 165 1 11 176 2 11 205 7 11 219 2 11 243 28 11 257 15 11 283 22 11 307 11 11 336 5 11 364 20 11 388 0 11 431 0 11 439 0 12 5 21 12 11 1 12 16 23 12 31 24 12 35 27 12 42 15 12 48 0 12 66 0 12 92 15 12 115 31 12 150 17 12 156 2 12 188 6 12 198 1 12 211 16 12 234 14 12 252 10 12 275 7 12 301 30 12 333 29 12 356 27 12 402 0 12 441 0 12 449 0 13 1 1 13 9 27 13 17 5 13 30 30 13 37 30 13 46 11 13 66 1 13 91 0 13 119 25 13 135 23 13 144 11 13 173 0 13 188 4 13 212 9 13 239 10 13 252 1 13 266 25 13 302 4 13 331 11 13 358 16 13 381 11 13 451 0 13 459 0 14 6 20 14 14 25 14 21 11 14 24 9 14 36 17 14 45 5 14 64 16 14 81 26 14 91 11 14 107 13 14 125 0 14 147 1 14 164 12 14 192 4 14 203 23 14 234 3 14 250 18 14 309 29 14 315 11 14 323 1 14 374 15 14 396 10 14 461 0 14 469 0 15 4 1 15 9 1 15 19 1 15 31 0 15 38 8 15 45 3 15 56 5 15 81 10 15 111 4 15 135 20 15 141 10 15 168 24 15 187 1 15 214 31 15 226 13 15 249 0 15 279 21 15 300 2 15 329 1 15 353 15 15 378 5 15 471 0 15 479 0 16 1 17 16 9 21 16 21 28 16 28 11 16 37 1 16 42 16 16 58 31 16 76 18 16 90 12 16 107 5 16 120 19 16 146 27 16 165 1 16 189 6 16 204 0 16 224 1 16 243 13 16 268 10 16 295 31 16 320 7 16 351 1 16 370 7 16 393 19 16 402 0 16 410 0 17 6 1 17 13 0 17 19 1 17 27 1 17 38 16 17 42 24 17 60 17 17 78 14 17 109 28 17 120 2 17 141 1 17 164 3 17 179 28 17 204 2 17 231 3 17 242 22 17 261 6 17 289 8 17 318 10 17 341 30 17 375 22 17 398 8 17 412 0 17 420 0 18 2 15 18 9 31 18 17 12 18 28 0 18 34 8 18 40 16 18 51 4 18 77 18 18 80 23 18 102 22 18 119 13 18 143 9 18 155 27 18 176 2 18 196 17 18 218 16 18 247 15 18 256 4 18 284 1 18 317 1 18 350 12 18 362 15 18 391 20 18 422 0 18 430 0 19 5 11 19 10 22 19 21 2 19 31 20 19 32 20 19 40 12 19 51 2 19 66 10 19 97 2 19 122 1 19 130 15 19 156 0 19 175 26 19 193 1 19 218 8 19 239 24 19 258 12 19 280 20 19 307 0 19 338 14 19 361 11 19 384 25 19 432 0 19 440 0 20 6 21 20 12 1 20 17 23 20 24 25 20 36 27 20 43 15 20 49 0 20 67 0 20 93 15 20 116 31 20 151 17 20 157 2 20 189 6 20 199 1 20 212 16 20 235 14 20 253 10 20 276 7 20 302 30 20 334 29 20 357 27 20 403 0 20 442 0 20 450 0 21 2 1 21 10 27 21 18 5 21 31 30 21 38 30 21 47 11 21 67 1 21 92 0 21 112 26 21 128 24 21 145 11 21 174 0 21 189 4 21 213 9 21 232 11 21 253 1 21 267 25 21 303 4 21 332 11 21 359 16 21 382 11 21 452 0 21 460 0 22 7 20 22 15 25 22 22 11 22 25 9 22 37 17 22 46 5 22 65 16 22 82 26 22 92 11 22 108 13 22 126 0 22 148 1 22 165 12 22 193 4 22 204 23 22 235 3 22 251 18 22 310 29 22 316 11 22 324 1 22 375 15 22 397 10 22 462 0 22 470 0 23 7 20 23 15 27 23 22 4 23 27 16 23 34 22 23 40 17 23 59 1 23 83 26 23 99 17 23 133 10 23 137 5 23 169 13 23 183 16 23 214 17 23 216 25 23 225 15 23 268 5 23 276 24 23 294 24 23 322 0 23 345 9 23 383 1 23 402 0 23 472 0 24 2 17 24 10 21 24 22 28 24 29 11 24 38 1 24 43 16 24 59 31 24 77 18 24 91 12 24 108 5 24 121 19 24 147 27 24 166 1 24 190 6 24 205 0 24 225 1 24 244 13 24 269 10 24 288 0 24 321 7 24 344 2 24 371 7 24 394 19 24 403 0 24 411 0 25 7 1 25 14 0 25 20 1 25 28 1 25 39 16 25 43 24 25 61 17 25 79 14 25 110 28 25 121 2 25 142 1 25 165 3 25 180 28 25 205 2 25 224 4 25 243 22 25 262 6 25 290 8 25 319 10 25 342 30 25 368 23 25 399 8 25 413 0 25 421 0 26 3 15 26 10 31 26 18 12 26 29 0 26 35 8 26 41 16 26 52 4 26 78 18 26 81 23 26 103 22 26 112 14 26 136 10 26 156 27 26 177 2 26 197 17 26 219 16 26 240 16 26 257 4 26 285 1 26 318 1 26 351 12 26 363 15 26 384 21 26 423 0 26 431 0 27 6 11 27 11 22 27 22 2 27 24 21 27 33 20 27 41 12 27 52 2 27 67 10 27 98 2 27 123 1 27 131 15 27 157 0 27 168 27 27 194 1 27 219 8 27 232 25 27 259 12 27 281 20 27 308 0 27 339 14 27 362 11 27 385 25 27 433 0 27 441 0 28 7 21 28 13 1 28 18 23 28 25 25 28 37 27 28 44 15 28 50 0 28 68 0 28 94 15 28 117 31 28 144 18 28 158 2 28 190 6 28 192 2 28 213 16 28 236 14 28 254 10 28 277 7 28 303 30 28 335 29 28 358 27 28 404 0 28 443 0 28 451 0 29 3 1 29 11 27 29 19 5 29 24 31 29 39 30 29 40 12 29 68 1 29 93 0 29 113 26 29 129 24 29 146 11 29 175 0 29 190 4 29 214 9 29 233 11 29 254 1 29 268 25 29 296 5 29 333 11 29 352 17 29 383 11 29 453 0 29 461 0 30 0 21 30 8 26 30 23 11 30 26 9 30 38 17 30 47 5 30 66 16 30 83 26 30 93 11 30 109 13 30 127 0 30 149 1 30 166 12 30 194 4 30 205 23 30 236 3 30 252 18 30 311 29 30 317 11 30 325 1 30 368 16 30 398 10 30 463 0 30 471 0 31 0 21 31 8 28 31 23 4 31 28 16 31 35 22 31 41 17 31 60 1 31 84 26 31 100 17 31 134 10 31 138 5 31 170 13 31 176 17 31 215 17 31 217 25 31 226 15 31 269 5 31 277 24 31 295 24 31 323 0 31 346 9 31 376 2 31 403 0 31 473 0 32 3 17 32 11 21 32 23 28 32 30 11 32 39 1 32 44 16 32 60 31 32 78 18 32 92 12 32 109 5 32 122 19 32 148 27 32 167 1 32 191 6 32 206 0 32 226 1 32 245 13 32 270 10 32 289 0 32 322 7 32 345 2 32 372 7 32 395 19 32 404 0 32 412 0 33 0 2 33 15 0 33 21 1 33 29 1 33 32 17 33 44 24 33 62 17 33 72 15 33 111 28 33 122 2 33 143 1 33 166 3 33 181 28 33 206 2 33 225 4 33 244 22 33 263 6 33 291 8 33 312 11 33 343 30 33 369 23 33 392 9 33 414 0 33 422 0 34 4 9 34 15 2 34 22 3 34 24 24 34 32 0 34 46 5 34 54 30 34 73 23 34 102 9 34 113 18 34 159 1 34 166 0 34 177 1 34 206 6 34 220 1 34 244 27 34 258 14 34 284 21 34 308 10 34 337 4 34 365 19 34 389 31 34 424 0 34 432 0 35 7 11 35 12 22 35 23 2 35 25 21 35 34 20 35 42 12 35 53 2 35 68 10 35 99 2 35 124 1 35 132 15 35 158 0 35 169 27 35 195 1 35 220 8 35 233 25 35 260 12 35 282 20 35 309 0 35 340 14 35 363 11 35 386 25 35 434 0 35 442 0 36 0 22 36 14 1 36 19 23 36 26 25 36 38 27 36 45 15 36 51 0 36 69 0 36 95 15 36 118 31 36 145 18 36 159 2 36 191 6 36 193 2 36 214 16 36 237 14 36 255 10 36 278 7 36 296 31 36 328 30 36 359 27 36 405 0 36 444 0 36 452 0 37 4 1 37 12 27 37 20 5 37 25 31 37 32 31 37 41 12 37 69 1 37 94 0 37 114 26 37 130 24 37 147 11 37 168 1 37 191 4 37 215 9 37 234 11 37 255 1 37 269 25 37 297 5 37 334 11 37 353 17 37 376 12 37 454 0 37 462 0 38 5 0 38 10 0 38 20 0 38 24 0 38 39 7 38 46 2 38 57 4 38 82 9 38 104 4 38 128 20 38 142 9 38 169 23 38 188 0 38 215 30 38 227 12 38 250 31 38 272 21 38 301 1 38 330 0 38 354 14 38 379 4 38 464 0 38 472 0 39 1 21 39 9 28 39 16 5 39 29 16 39 36 22 39 42 17 39 61 1 39 85 26 39 101 17 39 135 10 39 139 5 39 171 13 39 177 17 39 208 18 39 218 25 39 227 15 39 270 5 39 278 24 39 288 25 39 324 0 39 347 9 39 377 2 39 404 0 39 474 0 40 4 17 40 12 21 40 16 29 40 31 11 40 32 2 40 45 16 40 61 31 40 79 18 40 93 12 40 110 5 40 123 19 40 149 27 40 160 2 40 184 7 40 207 0 40 227 1 40 246 13 40 271 10 40 290 0 40 323 7 40 346 2 40 373 7 40 396 19 40 405 0 40 413 0 41 1 2 41 8 1 41 22 1 41 30 1 41 33 17 41 45 24 41 63 17 41 73 15 41 104 29 41 123 2 41 136 2 41 167 3 41 182 28 41 207 2 41 226 4 41 245 22 41 256 7 41 292 8 41 313 11 41 336 31 41 370 23 41 393 9 41 415 0 41 423 0 42 5 9 42 8 3 42 23 3 42 25 24 42 33 0 42 47 5 42 55 30 42 74 23 42 103 9 42 114 18 42 152 2 42 167 0 42 178 1 42 207 6 42 221 1 42 245 27 42 259 14 42 285 21 42 309 10 42 338 4 42 366 19 42 390 31 42 425 0 42 433 0 43 0 12 43 13 22 43 16 3 43 26 21 43 35 20 43 43 12 43 54 2 43 69 10 43 100 2 43 125 1 43 133 15 43 159 0 43 170 27 43 196 1 43 221 8 43 234 25 43 261 12 43 283 20 43 310 0 43 341 14 43 364 11 43 387 25 43 435 0 43 443 0 44 1 22 44 15 1 44 20 23 44 27 25 44 39 27 44 46 15 44 52 0 44 70 0 44 88 16 44 119 31 44 146 18 44 152 3 44 184 7 44 194 2 44 215 16 44 238 14 44 248 11 44 279 7 44 297 31 44 329 30 44 352 28 44 406 0 44 445 0 44 453 0 45 5 1 45 13 27 45 21 5 45 26 31 45 33 31 45 42 12 45 70 1 45 95 0 45 115 26 45 131 24 45 148 11 45 169 1 45 184 5 45 208 10 45 235 11 45 248 2 45 270 25 45 298 5 45 335 11 45 354 17 45 377 12 45 455 0 45 463 0 46 6 0 46 11 0 46 21 0 46 25 0 46 32 8 46 47 2 46 58 4 46 83 9 46 105 4 46 129 20 46 143 9 46 170 23 46 189 0 46 208 31 46 228 12 46 251 31 46 273 21 46 302 1 46 331 0 46 355 14 46 380 4 46 465 0 46 473 0 47 2 21 47 10 28 47 17 5 47 30 16 47 37 22 47 43 17 47 62 1 47 86 26 47 102 17 47 128 11 47 140 5 47 172 13 47 178 17 47 209 18 47 219 25 47 228 15 47 271 5 47 279 24 47 289 25 47 325 0 47 348 9 47 378 2 47 405 0 47 475 0 48 5 17 48 13 21 48 17 29 48 24 12 48 33 2 48 46 16 48 62 31 48 72 19 48 94 12 48 111 5 48 124 19 48 150 27 48 161 2 48 185 7 48 200 1 48 228 1 48 247 13 48 264 11 48 291 0 48 324 7 48 347 2 48 374 7 48 397 19 48 406 0 48 414 0 49 4 14 49 11 30 49 19 11 49 30 31 49 36 7 49 42 15 49 53 3 49 79 17 49 82 22 49 96 22 49 113 13 49 137 9 49 157 26 49 178 1 49 198 16 49 220 15 49 241 15 49 258 3 49 286 0 49 319 0 49 344 12 49 364 14 49 385 20 49 416 0 49 424 0 50 6 9 50 9 3 50 16 4 50 26 24 50 34 0 50 40 6 50 48 31 50 75 23 50 96 10 50 115 18 50 153 2 50 160 1 50 179 1 50 200 7 50 222 1 50 246 27 50 260 14 50 286 21 50 310 10 50 339 4 50 367 19 50 391 31 50 426 0 50 434 0 51 1 12 51 14 22 51 17 3 51 27 21 51 36 20 51 44 12 51 55 2 51 70 10 51 101 2 51 126 1 51 134 15 51 152 1 51 171 27 51 197 1 51 222 8 51 235 25 51 262 12 51 284 20 51 311 0 51 342 14 51 365 11 51 388 25 51 436 0 51 444 0 52 2 22 52 8 2 52 21 23 52 28 25 52 32 28 52 47 15 52 53 0 52 71 0 52 89 16 52 112 0 52 147 18 52 153 3 52 185 7 52 195 2 52 208 17 52 239 14 52 249 11 52 272 8 52 298 31 52 330 30 52 353 28 52 407 0 52 446 0 52 454 0 53 1 20 53 9 25 53 16 11 53 27 8 53 39 16 53 40 5 53 67 15 53 84 25 53 94 10 53 110 12 53 120 0 53 150 0 53 167 11 53 195 3 53 206 22 53 237 2 53 253 17 53 304 29 53 318 10 53 326 0 53 369 15 53 399 9 53 456 0 53 464 0 54 7 0 54 12 0 54 22 0 54 26 0 54 33 8 54 40 3 54 59 4 54 84 9 54 106 4 54 130 20 54 136 10 54 171 23 54 190 0 54 209 31 54 229 12 54 252 31 54 274 21 54 303 1 54 332 0 54 356 14 54 381 4 54 466 0 54 474 0 55 3 21 55 11 28 55 18 5 55 31 16 55 38 22 55 44 17 55 63 1 55 87 26 55 103 17 55 129 11 55 141 5 55 173 13 55 179 17 55 210 18 55 220 25 55 229 15 55 264 6 55 272 25 55 290 25 55 326 0 55 349 9 55 379 2 55 406 0 55 476 0 56 6 17 56 14 21 56 18 29 56 25 12 56 34 2 56 47 16 56 63 31 56 73 19 56 95 12 56 104 6 56 125 19 56 151 27 56 162 2 56 186 7 56 201 1 56 229 1 56 240 14 56 265 11 56 292 0 56 325 7 56 348 2 56 375 7 56 398 19 56 407 0 56 415 0 57 5 14 57 12 30 57 20 11 57 31 31 57 37 7 57 43 15 57 54 3 57 72 18 57 83 22 57 97 22 57 114 13 57 138 9 57 158 26 57 179 1 57 199 16 57 221 15 57 242 15 57 259 3 57 287 0 57 312 1 57 345 12 57 365 14 57 386 20 57 417 0 57 425 0 58 7 9 58 10 3 58 17 4 58 27 24 58 35 0 58 41 6 58 49 31 58 76 23 58 97 10 58 116 18 58 154 2 58 161 1 58 180 1 58 201 7 58 223 1 58 247 27 58 261 14 58 287 21 58 311 10 58 340 4 58 360 20 58 384 0 58 427 0 58 435 0 59 2 12 59 15 22 59 18 3 59 28 21 59 37 20 59 45 12 59 48 3 59 71 10 59 102 2 59 127 1 59 135 15 59 153 1 59 172 27 59 198 1 59 223 8 59 236 25 59 263 12 59 285 20 59 304 1 59 343 14 59 366 11 59 389 25 59 437 0 59 445 0 60 3 22 60 9 2 60 22 23 60 29 25 60 33 28 60 40 16 60 54 0 60 64 1 60 90 16 60 113 0 60 148 18 60 154 3 60 186 7 60 196 2 60 209 17 60 232 15 60 250 11 60 273 8 60 299 31 60 331 30 60 354 28 60 400 1 60 447 0 60 455 0 61 2 20 61 10 25 61 17 11 61 28 8 61 32 17 61 41 5 61 68 15 61 85 25 61 95 10 61 111 12 61 121 0 61 151 0 61 160 12 61 196 3 61 207 22 61 238 2 61 254 17 61 305 29 61 319 10 61 327 0 61 370 15 61 392 10 61 457 0 61 465 0 62 0 1 62 13 0 62 23 0 62 27 0 62 34 8 62 41 3 62 60 4 62 85 9 62 107 4 62 131 20 62 137 10 62 172 23 62 191 0 62 210 31 62 230 12 62 253 31 62 275 21 62 296 2 62 333 0 62 357 14 62 382 4 62 467 0 62 475 0 63 4 21 63 12 28 63 19 5 63 24 17 63 39 22 63 45 17 63 56 2 63 80 27 63 96 18 63 130 11 63 142 5 63 174 13 63 180 17 63 211 18 63 221 25 63 230 15 63 265 6 63 273 25 63 291 25 63 327 0 63 350 9 63 380 2 63 407 0 63 477 0 64 2 1 64 9 0 64 23 0 64 31 0 64 34 16 64 46 23 64 56 17 64 74 14 64 105 28 64 124 1 64 137 1 64 160 3 64 183 27 64 200 2 64 227 3 64 246 21 64 257 6 64 293 7 64 314 10 64 337 30 64 371 22 64 394 8 64 408 0 64 416 0 65 6 14 65 13 30 65 21 11 65 24 0 65 38 7 65 44 15 65 55 3 65 73 18 65 84 22 65 98 22 65 115 13 65 139 9 65 159 26 65 180 1 65 192 17 65 222 15 65 243 15 65 260 3 65 280 1 65 313 1 65 346 12 65 366 14 65 387 20 65 418 0 65 426 0 66 0 10 66 11 3 66 18 4 66 28 24 66 36 0 66 42 6 66 50 31 66 77 23 66 98 10 66 117 18 66 155 2 66 162 1 66 181 1 66 202 7 66 216 2 66 240 28 66 262 14 66 280 22 66 304 11 66 341 4 66 361 20 66 385 0 66 428 0 66 436 0 67 3 12 67 8 23 67 19 3 67 29 21 67 38 20 67 46 12 67 49 3 67 64 11 67 103 2 67 120 2 67 128 16 67 154 1 67 173 27 67 199 1 67 216 9 67 237 25 67 256 13 67 286 20 67 305 1 67 336 15 67 367 11 67 390 25 67 438 0 67 446 0 68 6 0 68 14 26 68 22 4 68 27 30 68 34 30 68 43 11 68 71 0 68 88 0 68 116 25 68 132 23 68 149 10 68 170 0 68 185 4 68 209 9 68 236 10 68 249 1 68 271 24 68 299 4 68 328 11 68 355 16 68 378 11 68 448 0 68 456 0 69 3 20 69 11 25 69 18 11 69 29 8 69 33 17 69 42 5 69 69 15 69 86 25 69 88 11 69 104 13 69 122 0 69 144 1 69 161 12 69 197 3 69 200 23 69 239 2 69 255 17 69 306 29 69 312 11 69 320 1 69 371 15 69 393 10 69 458 0 69 466 0 70 1 1 70 14 0 70 16 1 70 28 0 70 35 8 70 42 3 70 61 4 70 86 9 70 108 4 70 132 20 70 138 10 70 173 23 70 184 1 70 211 31 70 231 12 70 254 31 70 276 21 70 297 2 70 334 0 70 358 14 70 383 4 70 468 0 70 476 0 71 5 21 71 13 28 71 20 5 71 25 17 71 32 23 71 46 17 71 57 2 71 81 27 71 97 18 71 131 11 71 143 5 71 175 13 71 181 17 71 212 18 71 222 25 71 231 15 71 266 6 71 274 25 71 292 25 71 320 1 71 351 9 71 381 2 71 400 1 71 478 0 72 3 1 72 10 0 72 16 1 72 24 1 72 35 16 72 47 23 72 57 17 72 75 14 72 106 28 72 125 1 72 138 1 72 161 3 72 176 28 72 201 2 72 228 3 72 247 21 72 258 6 72 294 7 72 315 10 72 338 30 72 372 22 72 395 8 72 409 0 72 417 0 73 7 14 73 14 30 73 22 11 73 25 0 73 39 7 73 45 15 73 48 4 73 74 18 73 85 22 73 99 22 73 116 13 73 140 9 73 152 27 73 181 1 73 193 17 73 223 15 73 244 15 73 261 3 73 281 1 73 314 1 73 347 12 73 367 14 73 388 20 73 419 0 73 427 0 74 1 10 74 12 3 74 19 4 74 29 24 74 37 0 74 43 6 74 51 31 74 78 23 74 99 10 74 118 18 74 156 2 74 163 1 74 182 1 74 203 7 74 217 2 74 241 28 74 263 14 74 281 22 74 305 11 74 342 4 74 362 20 74 386 0 74 429 0 74 437 0 75 4 12 75 9 23 75 20 3 75 30 21 75 39 20 75 47 12 75 50 3 75 65 11 75 96 3 75 121 2 75 129 16 75 155 1 75 174 27 75 192 2 75 217 9 75 238 25 75 257 13 75 287 20 75 306 1 75 337 15 75 360 12 75 391 25 75 439 0 75 447 0 76 7 0 76 15 26 76 23 4 76 28 30 76 35 30 76 44 11 76 64 1 76 89 0 76 117 25 76 133 23 76 150 10 76 171 0 76 186 4 76 210 9 76 237 10 76 250 1 76 264 25 76 300 4 76 329 11 76 356 16 76 379 11 76 449 0 76 457 0 77 4 20 77 12 25 77 19 11 77 30 8 77 34 17 77 43 5 77 70 15 77 87 25 77 89 11 77 105 13 77 123 0 77 145 1 77 162 12 77 198 3 77 201 23 77 232 3 77 248 18 77 307 29 77 313 11 77 321 1 77 372 15 77 394 10 77 459 0 77 467 0 78 2 1 78 15 0 78 17 1 78 29 0 78 36 8 78 43 3 78 62 4 78 87 9 78 109 4 78 133 20 78 139 10 78 174 23 78 185 1 78 212 31 78 224 13 78 255 31 78 277 21 78 298 2 78 335 0 78 359 14 78 376 5 78 469 0 78 477 0 79 6 21 79 14 28 79 21 5 79 26 17 79 33 23 79 47 17 79 58 2 79 82 27 79 98 18 79 132 11 79 136 6 79 168 14 79 182 17 79 213 18 79 223 25 79 224 16 79 267 6 79 275 25 79 293 25 79 321 1 79 344 10 79 382 2 79 401 1 79 479 0

APPENDIX TABLE I Specification of the base matrix B_(13/15) for the rate- 13/15 LDPC code 0 2 15 0 9 6 0 21 0 0 25 1 0 48 11 0 81 29 0 90 5 0 108 11 0 119 19 0 121 12 0 145 30 0 166 9 0 181 18 0 189 11 0 196 5 0 214 8 0 225 11 0 261 19 0 266 3 0 284 11 0 310 0 0 335 1 0 349 7 0 368 20 0 390 10 0 409 0 0 416 0 0 424 0 1 3 23 1 10 27 1 17 28 1 26 3 1 52 5 1 63 0 1 84 26 1 94 21 1 108 6 1 125 27 1 147 22 1 164 11 1 178 8 1 193 4 1 208 3 1 224 1 1 242 1 1 270 4 1 283 10 1 304 0 1 327 9 1 347 0 1 374 3 1 384 17 1 412 21 1 424 0 1 432 0 2 1 0 2 8 5 2 21 1 2 29 26 2 41 1 2 49 2 2 71 21 2 81 28 2 110 14 2 127 23 2 141 4 2 157 30 2 179 21 2 207 17 2 208 29 2 225 20 2 238 19 2 261 6 2 277 2 2 299 18 2 319 22 2 341 29 2 365 4 2 397 21 2 404 27 2 432 0 2 440 0 3 4 1 3 11 0 3 17 1 3 31 1 3 41 13 3 69 28 3 87 19 3 100 4 3 110 25 3 141 0 3 152 24 3 167 6 3 173 29 3 188 13 3 203 15 3 225 18 3 239 3 3 260 1 3 274 27 3 301 2 3 316 0 3 339 0 3 362 31 3 380 28 3 401 3 3 440 0 3 448 0 4 7 12 4 11 2 4 18 14 4 28 6 4 38 0 4 50 6 4 67 18 4 74 23 4 96 20 4 134 0 4 138 0 4 153 13 4 171 14 4 190 1 4 207 3 4 218 4 4 240 3 4 249 11 4 274 0 4 292 24 4 317 28 4 329 11 4 356 12 4 392 3 4 417 0 4 448 0 4 456 0 5 3 3 5 10 0 5 17 5 5 26 4 5 32 25 5 62 6 5 79 29 5 89 25 5 118 0 5 132 2 5 142 26 5 149 7 5 163 0 5 177 5 5 206 9 5 221 4 5 234 18 5 249 0 5 283 23 5 321 12 5 335 18 5 351 12 5 370 10 5 389 10 5 408 26 5 456 0 5 464 0 6 12 25 6 22 15 6 27 2 6 39 17 6 46 16 6 60 29 6 77 2 6 98 8 6 116 6 6 131 24 6 147 4 6 170 23 6 195 20 6 210 29 6 218 23 6 247 7 6 250 7 6 295 31 6 303 10 6 305 5 6 353 0 6 363 3 6 380 18 6 407 9 6 464 0 6 472 0 7 3 27 7 32 2 7 41 22 7 56 4 7 65 8 7 76 27 7 94 4 7 98 18 7 116 13 7 125 12 7 129 2 7 156 6 7 168 10 7 188 21 7 199 20 7 223 21 7 234 3 7 244 30 7 268 13 7 289 30 7 321 18 7 338 5 7 358 1 7 379 21 7 396 1 7 418 0 7 472 0 8 3 15 8 10 6 8 22 0 8 26 1 8 49 11 8 82 29 8 91 5 8 109 11 8 112 20 8 122 12 8 146 30 8 167 9 8 182 18 8 190 11 8 197 5 8 215 8 8 226 11 8 262 19 8 267 3 8 285 11 8 311 0 8 328 2 8 350 7 8 369 20 8 391 10 8 410 0 8 417 0 8 425 0 9 4 23 9 11 27 9 18 28 9 27 3 9 53 5 9 56 1 9 85 26 9 95 21 9 109 6 9 126 27 9 148 22 9 165 11 9 179 8 9 194 4 9 209 3 9 225 1 9 243 1 9 271 4 9 284 10 9 305 0 9 320 10 9 348 0 9 375 3 9 385 17 9 413 21 9 425 0 9 433 0 10 2 0 10 9 5 10 22 1 10 30 26 10 42 1 10 50 2 10 64 22 10 82 28 10 111 14 10 120 24 10 142 4 10 158 30 10 180 21 10 200 18 10 209 29 10 226 20 10 239 19 10 262 6 10 278 2 10 300 18 10 312 23 10 342 29 10 366 4 10 398 21 10 405 27 10 433 0 10 441 0 11 5 1 11 12 0 11 18 1 11 24 2 11 42 13 11 70 28 11 80 20 11 101 4 11 111 25 11 142 0 11 153 24 11 160 7 11 174 29 11 189 13 11 204 15 11 226 18 11 232 4 11 261 1 11 275 27 11 302 2 11 317 0 11 340 0 11 363 31 11 381 28 11 402 3 11 441 0 11 449 0 12 0 13 12 12 2 12 19 14 12 29 6 12 39 0 12 51 6 12 68 18 12 75 23 12 97 20 12 135 0 12 139 0 12 154 13 12 172 14 12 191 1 12 200 4 12 219 4 12 241 3 12 250 11 12 275 0 12 293 24 12 318 28 12 330 11 12 357 12 12 393 3 12 418 0 12 449 0 12 457 0 13 4 3 13 11 0 13 18 5 13 27 4 13 33 25 13 63 6 13 72 30 13 90 25 13 119 0 13 133 2 13 143 26 13 150 7 13 164 0 13 178 5 13 207 9 13 222 4 33 235 18 13 250 0 13 284 23 13 322 12 13 328 19 13 344 13 13 371 10 13 390 10 13 409 26 13 457 0 13 465 0 14 13 25 14 23 15 14 28 2 14 32 18 14 47 16 14 61 29 14 78 2 14 99 8 14 117 6 14 132 24 14 148 4 14 171 23 14 196 20 14 211 29 14 219 23 14 240 8 14 251 7 14 288 0 14 296 11 14 306 5 14 354 0 14 364 3 14 381 18 14 400 10 14 465 0 14 473 0 15 4 27 15 33 2 15 42 22 15 57 4 15 66 8 15 77 27 15 95 4 15 99 18 15 117 13 15 126 12 15 130 2 15 157 6 15 169 10 15 189 21 15 192 21 15 216 22 15 235 3 15 245 30 15 269 13 15 290 30 15 322 18 15 339 5 15 359 1 15 380 21 15 397 1 15 419 0 15 473 0 16 4 15 16 11 6 16 23 0 16 27 1 16 50 11 16 83 29 16 92 5 16 110 11 16 113 20 16 123 12 16 147 30 16 160 10 16 183 18 16 191 11 16 198 5 16 208 9 16 227 11 16 263 19 16 268 3 16 286 11 16 304 1 16 329 2 16 351 7 16 370 20 16 384 11 16 411 0 16 418 0 16 426 0 17 5 23 17 12 27 17 19 28 17 28 3 17 54 5 17 57 1 17 86 26 17 88 22 17 110 6 17 127 27 17 149 22 17 166 11 17 180 8 17 195 4 17 210 3 17 226 1 17 244 1 17 264 5 17 285 10 17 306 0 17 321 10 17 349 0 17 368 4 17 386 17 17 414 21 17 426 0 17 434 0 18 3 0 18 10 5 18 23 1 18 31 26 18 43 1 18 51 2 18 65 22 18 83 28 18 104 15 18 121 24 18 143 4 18 159 30 18 181 21 18 201 18 18 210 29 18 227 20 18 232 20 18 263 6 18 279 2 18 301 18 18 313 23 18 343 29 18 367 4 18 399 21 18 406 27 18 434 0 18 442 0 19 6 1 19 13 0 19 19 1 19 25 2 19 43 13 19 71 28 19 81 20 19 102 4 19 104 26 19 143 0 19 154 24 19 161 7 19 175 29 19 190 13 19 205 15 19 227 18 19 233 4 19 262 1 19 276 27 19 303 2 19 318 0 19 341 0 19 364 31 19 382 28 19 403 3 19 442 0 19 450 0 20 1 13 20 13 2 20 20 14 20 30 6 20 32 1 20 52 6 20 69 18 20 76 23 20 98 20 20 128 1 20 140 0 20 155 13 20 173 14 20 184 2 20 201 4 20 220 4 20 242 3 20 251 11 20 276 0 20 294 24 20 319 28 20 331 11 20 358 12 20 394 3 20 419 0 20 450 0 20 458 0 21 5 3 21 12 0 21 19 5 21 28 4 21 34 25 21 56 7 21 73 30 21 91 25 21 112 1 21 134 2 21 136 27 21 151 7 21 165 0 21 179 5 21 200 10 21 223 4 21 236 18 21 251 0 21 285 23 21 323 12 21 329 19 21 345 13 21 372 10 21 391 10 21 410 26 21 458 0 21 466 0 22 14 25 22 16 16 22 29 2 22 33 18 22 40 17 22 62 29 22 79 2 22 100 8 22 118 6 22 133 24 22 149 4 22 172 23 22 197 20 22 212 29 22 220 23 22 241 8 22 252 7 22 289 0 22 297 11 22 307 5 22 355 0 22 365 3 22 382 18 22 401 10 22 466 0 22 474 0 23 5 27 23 34 2 23 43 22 23 58 4 23 67 8 23 78 27 23 88 5 23 100 18 23 118 13 23 127 12 23 131 2 23 158 6 23 170 10 23 190 21 23 193 21 23 217 22 23 236 3 23 246 30 23 270 13 23 291 30 23 323 18 23 340 5 23 352 2 23 381 21 23 398 1 23 420 0 23 474 0 24 5 15 24 12 6 24 16 1 24 28 1 24 51 11 24 84 29 24 93 5 24 111 11 24 114 20 24 124 12 24 148 30 24 161 10 24 176 19 24 184 12 24 199 5 24 209 9 24 228 11 24 256 20 24 269 3 24 287 11 24 305 1 24 330 2 24 344 8 24 371 20 24 385 11 24 412 0 24 419 0 24 427 0 25 6 23 25 13 27 25 20 28 25 29 3 25 55 5 25 58 1 25 87 26 25 89 22 25 111 6 25 120 28 25 150 22 25 167 11 25 181 8 25 196 4 25 211 3 25 227 1 25 245 1 25 265 5 25 286 10 25 307 0 25 322 10 25 350 0 25 369 4 25 387 17 25 415 21 25 427 0 25 435 0 26 4 0 26 11 5 26 16 2 26 24 27 26 44 1 26 52 2 26 66 22 26 84 28 26 105 15 26 122 24 26 136 5 26 152 31 26 182 21 26 202 18 26 211 29 26 228 20 26 233 20 26 256 7 26 272 3 26 302 18 26 314 23 26 336 30 26 360 5 26 392 22 26 407 27 26 435 0 26 443 0 27 7 1 27 14 0 27 20 1 27 26 2 27 44 13 27 64 29 27 82 20 27 103 4 27 105 26 27 136 1 27 155 24 27 162 7 27 168 30 27 191 13 27 206 15 27 228 18 27 234 4 27 263 1 27 277 27 27 296 3 27 319 0 27 342 0 27 365 31 27 383 28 27 404 3 27 443 0 27 451 0 28 2 13 28 14 2 28 21 14 28 31 6 28 33 1 28 53 6 28 70 18 28 77 23 28 99 20 28 129 1 28 141 0 28 156 13 28 174 14 28 185 2 28 202 4 28 221 4 28 243 3 28 252 11 28 277 0 28 295 24 28 312 29 28 332 11 28 359 12 28 395 3 28 420 0 28 451 0 28 459 0 29 6 3 29 13 0 29 20 5 29 29 4 29 35 25 29 57 7 29 74 30 29 92 25 29 113 1 29 135 2 29 137 27 29 144 8 29 166 0 29 180 5 29 201 10 29 216 5 29 237 18 29 252 0 29 286 23 29 324 12 29 330 19 29 346 13 29 373 10 29 384 11 29 411 26 29 459 0 29 467 0 30 15 25 30 17 16 30 30 2 30 34 18 30 41 17 30 63 29 30 72 3 30 101 8 30 119 6 30 134 24 30 150 4 30 173 23 30 198 20 30 213 29 30 221 23 30 242 8 30 253 7 30 290 0 30 298 11 30 308 5 30 356 0 30 366 3 30 383 18 30 402 10 30 467 0 30 475 0 31 6 27 31 35 2 31 44 22 31 59 4 31 68 8 31 79 27 31 89 5 31 101 18 31 119 13 31 120 13 31 132 2 31 159 6 31 171 10 31 191 21 31 194 21 31 218 22 31 237 3 31 247 30 31 271 13 31 292 30 31 324 18 31 341 5 31 353 2 31 382 21 31 399 1 31 421 0 31 475 0 32 6 15 32 13 6 32 17 1 32 29 1 32 52 11 32 85 29 32 94 5 32 104 12 32 115 20 32 125 12 32 149 30 32 162 10 32 177 19 32 185 12 32 192 6 32 210 9 32 229 11 32 257 20 32 270 3 32 280 12 32 306 1 32 331 2 32 345 8 32 372 20 32 386 11 32 413 0 32 420 0 32 428 0 33 7 23 33 14 27 33 21 28 33 30 3 33 48 6 33 59 1 33 80 27 33 90 22 33 104 7 33 121 28 33 151 22 33 160 12 33 182 8 33 197 4 33 212 3 33 228 1 33 246 1 33 266 5 33 287 10 33 308 0 33 323 10 33 351 0 33 370 4 33 388 17 33 408 22 33 428 0 33 436 0 34 5 0 34 12 5 34 17 2 34 25 27 34 45 1 34 53 2 34 67 22 34 85 28 34 106 15 34 123 24 34 137 5 34 153 31 34 183 21 34 203 18 34 212 29 34 229 20 34 234 20 34 257 7 34 273 3 34 303 18 34 315 23 34 337 30 34 361 5 34 393 22 34 400 28 34 436 0 34 444 0 35 0 2 35 15 0 35 21 1 35 27 2 35 45 13 35 65 29 35 83 20 35 96 5 35 106 26 35 137 1 35 156 24 35 163 7 35 169 30 35 184 14 35 207 15 35 229 18 35 235 4 35 256 2 35 278 27 35 297 3 35 312 1 35 343 0 35 366 31 35 376 29 35 405 3 35 444 0 35 452 0 36 3 13 36 15 2 36 22 14 36 24 7 36 34 1 36 54 6 36 71 18 36 78 23 36 100 20 36 130 1 36 142 0 36 157 13 36 175 14 36 186 2 36 203 4 36 222 4 36 244 3 36 253 11 36 278 0 36 288 25 36 313 29 36 333 11 36 352 13 36 396 3 36 421 0 36 452 0 36 460 0 37 7 3 37 14 0 37 21 5 37 30 4 37 36 25 37 58 7 37 75 30 37 93 25 37 114 1 37 128 3 37 138 27 37 145 8 37 167 0 37 181 5 37 202 10 37 217 5 37 238 18 37 253 0 37 287 23 37 325 12 37 331 19 37 347 13 37 374 10 37 385 11 37 412 26 37 460 0 37 468 0 38 8 26 38 18 16 38 31 2 38 35 18 38 42 17 38 56 30 38 73 3 38 102 8 38 112 7 38 135 24 38 151 4 38 174 23 38 199 20 38 214 29 38 222 23 38 243 8 38 254 7 38 291 0 38 299 11 38 309 5 38 357 0 38 367 3 38 376 19 38 403 10 38 468 0 38 476 0 39 7 27 39 36 2 39 45 22 39 60 4 39 69 8 39 72 28 39 90 5 39 102 18 39 112 14 39 121 13 39 133 2 39 152 7 39 172 10 39 184 22 39 195 21 39 219 22 39 238 3 39 240 31 39 264 14 39 293 30 39 325 18 39 342 5 39 354 2 39 383 21 39 392 2 39 422 0 39 476 0 40 7 15 40 14 6 40 18 1 40 30 1 40 53 11 40 86 29 40 95 5 40 105 12 40 116 20 40 126 12 40 150 30 40 163 10 40 178 19 40 186 12 40 193 6 40 211 9 40 230 11 40 258 20 40 271 3 40 281 12 40 307 1 40 332 2 40 346 8 40 373 20 40 387 11 40 414 0 40 421 0 40 429 0 41 0 24 41 15 27 41 22 28 41 31 3 41 49 6 41 60 1 41 81 27 41 91 22 41 105 7 41 122 28 41 144 23 41 161 12 41 183 8 41 198 4 41 213 3 41 229 1 43 247 1 41 267 5 41 280 11 41 309 0 41 324 10 41 344 1 41 371 4 41 389 17 41 409 22 41 429 0 41 437 0 42 6 0 42 13 5 42 18 2 42 26 27 42 46 1 42 54 2 42 68 22 42 86 28 42 107 15 42 124 24 42 138 5 42 154 31 42 176 22 42 204 18 42 213 29 42 230 20 42 235 20 42 258 7 42 274 3 42 296 19 42 316 23 42 338 30 42 362 5 42 394 22 42 401 28 42 437 0 42 445 0 43 1 2 43 8 1 43 22 1 43 28 2 43 46 13 43 66 29 43 84 20 43 97 5 43 107 26 43 138 1 43 157 24 43 164 7 43 170 30 43 185 14 43 200 16 43 230 18 43 236 4 43 257 2 43 279 27 43 298 3 43 313 1 43 336 1 43 367 31 43 377 29 43 406 3 43 445 0 43 453 0 44 4 13 44 8 3 44 23 14 44 25 7 44 35 1 44 55 6 44 64 19 44 79 23 44 101 20 44 131 1 44 143 0 44 158 13 44 168 15 44 187 2 44 204 4 44 223 4 44 245 3 44 254 11 44 279 0 44 289 25 44 314 29 44 334 11 44 353 13 44 397 3 44 422 0 44 453 0 44 461 0 45 0 4 45 15 0 45 22 5 45 31 4 45 37 25 45 59 7 45 76 30 45 94 25 45 115 1 45 129 3 45 139 27 45 146 8 45 160 1 45 182 5 45 203 10 45 218 5 45 239 18 45 254 0 45 280 24 45 326 12 45 332 19 45 348 13 45 375 10 45 386 11 45 413 26 45 461 0 45 469 0 46 9 26 46 19 16 46 24 3 46 36 18 46 43 17 46 57 30 46 74 3 46 103 8 46 113 7 46 128 25 46 144 5 46 175 23 46 192 21 46 215 29 46 223 23 46 244 8 46 255 7 46 292 0 46 300 11 46 310 5 46 358 0 46 360 4 46 377 19 46 404 10 46 469 0 46 477 0 47 0 28 47 37 2 47 46 22 47 61 4 47 70 8 47 73 28 47 91 5 47 103 18 47 113 14 47 122 13 47 134 2 47 153 7 47 173 10 47 185 22 47 196 21 47 220 22 47 239 3 47 241 31 47 265 14 47 294 30 47 326 18 47 343 5 47 355 2 47 376 22 47 393 2 47 423 0 47 477 0 48 0 16 48 15 6 48 19 1 48 31 1 48 54 11 48 87 29 48 88 6 48 106 12 48 117 20 48 127 12 48 151 30 48 164 10 48 179 19 48 187 12 48 194 6 48 212 9 48 231 11 48 259 20 48 264 4 48 282 12 48 308 1 48 333 2 48 347 8 48 374 20 48 388 11 48 415 0 48 422 0 48 430 0 49 1 24 49 8 28 49 23 28 49 24 4 49 50 6 49 61 1 49 82 27 49 92 22 49 106 7 49 123 28 49 145 23 49 162 12 49 176 9 49 199 4 49 214 3 49 230 1 49 240 2 49 268 5 49 281 11 49 310 0 49 325 10 49 345 1 49 372 4 49 390 17 49 410 22 49 430 0 49 438 0 50 7 0 50 14 5 50 19 2 50 27 27 50 47 1 50 55 2 50 69 22 50 87 28 50 108 15 50 125 24 50 139 5 50 155 31 50 177 22 50 205 18 50 214 29 50 231 20 50 236 20 50 259 7 50 275 3 50 297 19 50 317 23 50 339 30 50 363 5 50 395 22 50 402 28 50 438 0 50 446 0 51 2 2 51 9 1 51 23 1 51 29 2 51 47 13 51 67 29 51 85 20 51 98 5 51 108 26 51 139 1 51 158 24 51 165 7 51 171 30 51 186 14 51 201 16 51 231 18 51 237 4 51 258 2 51 272 28 51 299 3 51 314 1 51 337 1 51 360 0 51 378 29 51 407 3 51 446 0 51 454 0 52 5 13 52 9 3 52 16 15 52 26 7 52 36 1 52 48 7 52 65 19 52 72 24 52 102 20 52 132 1 52 136 1 52 159 13 52 169 15 52 188 2 52 205 4 52 216 5 52 246 3 52 255 11 52 272 1 52 290 25 52 315 29 52 335 11 52 354 13 52 398 3 52 423 0 52 454 0 52 462 0 53 1 4 53 8 1 53 23 5 53 24 5 53 38 25 53 60 7 53 77 30 53 95 25 53 116 1 53 130 3 53 140 27 53 147 8 53 161 1 53 183 5 53 204 10 53 219 5 53 232 19 53 255 0 53 281 24 53 327 12 53 333 19 53 349 13 53 368 11 53 387 11 53 414 26 53 462 0 53 470 0 54 10 26 54 20 16 54 25 3 54 37 18 54 44 17 54 58 30 54 75 3 54 96 9 54 114 7 54 129 25 54 145 5 54 168 24 54 193 21 54 208 30 54 216 24 54 245 8 54 248 8 54 293 0 54 301 11 54 311 5 54 359 0 54 361 4 54 378 19 54 405 10 54 470 0 54 478 0 55 1 28 55 38 2 55 47 22 55 62 4 55 71 8 55 74 28 55 92 5 55 96 19 55 114 14 55 123 13 55 135 2 55 154 7 55 174 10 55 186 22 55 197 21 55 221 22 55 232 4 55 242 31 55 266 14 55 295 30 55 327 18 55 336 6 55 356 2 55 377 22 55 394 2 55 416 1 55 478 0 56 1 16 56 8 7 56 20 1 56 24 2 56 55 11 56 80 30 56 89 6 56 107 12 56 118 20 56 120 13 56 144 31 56 165 10 56 180 19 56 188 12 56 195 6 56 213 9 56 224 12 56 260 20 56 265 4 56 283 12 56 309 1 56 334 2 56 348 8 56 375 20 56 389 11 56 408 1 56 423 0 56 431 0 57 2 24 57 9 28 57 16 29 57 25 4 57 51 6 57 62 1 57 83 27 57 93 22 57 107 7 57 124 28 57 146 23 57 163 12 57 177 9 57 192 5 57 215 3 57 231 1 57 241 2 57 269 5 57 282 11 57 311 0 57 326 10 57 346 1 57 373 4 57 391 17 57 411 22 57 431 0 57 439 0 58 0 1 58 15 5 58 20 2 58 28 27 58 40 2 58 48 3 58 70 22 58 80 29 58 109 15 58 126 24 58 140 5 58 156 31 58 178 22 58 206 18 58 215 29 58 224 21 58 237 20 58 260 7 58 276 3 58 298 19 58 318 23 58 340 30 58 364 5 58 396 22 58 403 28 58 439 0 58 447 0 59 3 2 59 10 1 59 16 2 59 30 2 59 40 14 59 68 29 59 86 20 59 99 5 59 109 26 59 140 1 59 159 24 59 166 7 59 172 30 59 187 14 59 202 16 59 224 19 59 238 4 59 259 2 59 273 28 59 300 3 59 315 1 59 338 1 59 361 0 59 379 29 59 400 4 59 447 0 59 455 0 60 6 13 60 30 3 60 17 15 60 27 7 60 37 1 60 49 7 60 66 19 60 73 24 60 103 20 60 133 1 60 137 1 60 152 14 60 170 15 60 189 2 60 206 4 60 217 5 60 247 3 60 248 12 60 273 1 60 291 25 60 316 29 60 328 12 60 355 13 60 399 3 60 416 1 60 455 0 60 463 0 61 2 4 61 9 1 61 16 6 61 25 5 61 39 25 61 61 7 61 78 30 61 88 26 61 117 1 61 131 3 61 141 27 61 148 8 61 162 1 61 176 6 61 205 10 61 220 5 61 233 19 61 248 1 61 282 24 61 320 13 61 334 19 61 350 13 61 369 11 61 388 11 61 415 26 61 463 0 61 471 0 62 11 26 62 21 16 62 26 3 62 38 18 62 45 17 62 59 30 62 76 3 62 97 9 62 115 7 62 130 25 62 146 5 62 169 24 62 194 21 62 209 30 62 217 24 62 246 8 62 249 8 62 294 0 62 302 11 62 304 6 62 352 1 62 362 4 62 379 19 62 406 10 62 471 0 62 479 0 63 2 28 63 39 2 63 40 23 63 63 4 63 64 9 63 75 28 63 93 5 63 97 19 63 115 14 63 124 13 63 128 3 63 155 7 63 175 10 63 187 22 63 198 21 63 222 22 63 233 4 63 243 31 63 267 14 63 288 31 63 320 19 63 337 6 63 357 2 63 378 22 63 395 2 63 417 1 63 479 0

APPENDIX TABLE J Specification of the base matrix B_(9/10) for the rate- 9/10 LDPC code 0 13 0 0 16 0 0 33 1 0 46 22 0 56 0 0 65 30 0 80 0 0 92 29 0 134 27 0 144 17 0 161 9 0 174 29 0 187 22 0 197 18 0 204 28 0 209 26 0 227 16 0 238 7 0 245 8 0 249 5 0 263 22 0 270 29 0 274 16 0 282 5 0 308 14 0 318 1 0 325 0 0 331 19 0 347 11 0 361 29 0 382 28 0 400 22 0 423 13 0 426 29 0 432 0 0 440 0 1 11 1 1 22 0 1 39 1 1 44 23 1 62 0 1 71 30 1 86 0 1 90 30 1 132 28 1 150 17 1 167 9 1 172 30 1 185 23 1 195 19 1 202 29 1 215 26 1 225 17 1 236 8 1 243 9 1 255 5 1 261 23 1 268 30 1 272 17 1 280 6 1 306 15 1 316 2 1 323 1 1 329 20 1 345 12 1 367 29 1 380 29 1 406 22 1 421 14 1 424 30 1 438 0 1 446 0 2 14 20 2 21 1 2 34 14 2 45 0 2 59 9 2 69 0 2 80 8 2 94 0 2 104 7 2 116 1 2 131 19 2 139 4 2 145 1 2 167 20 2 175 15 2 183 2 2 184 5 2 192 23 2 212 16 2 226 24 2 242 17 2 256 15 2 265 30 2 283 2 2 299 29 2 305 3 2 313 13 2 329 25 2 344 7 2 363 3 2 381 3 2 393 9 2 413 25 2 425 19 2 444 0 2 452 0 3 7 18 3 18 4 3 30 18 3 43 1 3 50 27 3 70 1 3 78 24 3 94 0 3 99 29 3 113 2 3 122 0 3 134 5 3 148 0 3 158 0 3 161 26 3 172 9 3 199 18 3 208 6 3 222 9 3 225 4 3 244 0 3 261 22 3 264 4 3 285 30 3 294 11 3 317 8 3 321 4 3 335 15 3 349 8 3 366 27 3 380 22 3 393 4 3 414 1 3 422 21 3 450 0 3 458 0 4 0 0 4 21 14 4 28 0 4 44 11 4 51 0 4 66 4 4 73 0 4 91 1 4 99 0 4 105 19 4 124 9 4 135 2 4 141 10 4 158 1 4 182 2 4 192 26 4 201 10 4 214 15 4 223 8 4 231 20 4 239 21 4 254 25 4 274 29 4 280 17 4 290 2 4 303 4 4 318 10 4 343 17 4 358 30 4 374 12 4 389 27 4 395 27 4 411 1 4 433 0 4 456 0 4 464 0 5 6 0 5 19 15 5 26 1 5 42 12 5 49 1 5 64 5 5 79 0 5 89 2 5 97 1 5 111 19 5 122 10 5 133 3 5 139 11 5 156 2 5 180 3 5 198 26 5 207 10 5 212 16 5 221 9 5 229 21 5 237 22 5 252 26 5 272 30 5 286 17 5 288 3 5 301 5 5 316 11 5 341 18 5 356 31 5 372 13 5 387 28 5 393 28 5 409 2 5 439 0 5 462 0 5 470 0 6 7 3 6 15 15 6 24 7 6 35 31 6 52 0 6 56 10 6 72 2 6 87 13 6 99 1 6 110 0 6 117 0 6 122 27 6 138 2 6 157 28 6 161 2 6 174 0 6 181 22 6 188 26 6 205 7 6 220 10 6 239 6 6 251 29 6 258 9 6 273 23 6 292 11 6 302 0 6 311 7 6 322 3 6 340 13 6 356 21 6 372 27 6 385 31 6 400 6 6 429 23 6 468 0 6 476 0 7 3 7 7 9 0 7 24 3 7 35 23 7 50 1 7 63 4 7 78 7 7 84 16 7 99 0 7 110 30 7 118 0 7 125 22 7 138 10 7 151 17 7 152 9 7 176 5 7 190 4 7 204 0 7 223 29 7 232 12 7 245 26 7 255 8 7 268 21 7 274 0 7 295 0 7 303 2 7 305 14 7 327 3 7 340 2 7 356 0 7 371 7 7 385 6 7 404 7 7 416 27 7 436 0 7 474 0 8 14 0 8 17 0 8 34 1 8 47 22 8 57 0 8 66 30 8 81 0 8 93 29 8 135 27 8 145 17 8 162 9 8 175 29 8 188 22 8 198 18 8 205 28 8 210 26 8 228 16 8 239 7 8 246 8 8 250 5 8 256 23 8 271 29 8 275 16 8 283 5 8 309 14 8 319 1 8 326 0 8 332 19 8 348 11 8 362 29 8 383 28 8 401 22 8 416 14 8 427 29 8 433 0 8 441 0 9 12 1 9 23 0 9 32 2 9 45 23 9 63 0 9 64 31 9 87 0 9 91 30 9 133 28 9 151 17 9 160 10 9 173 30 9 186 23 9 196 19 9 203 29 9 208 27 9 226 17 9 237 8 9 244 9 9 248 6 9 262 23 9 269 30 9 273 17 9 281 6 9 307 15 9 317 2 9 324 1 9 330 20 9 346 12 9 360 30 9 381 29 9 407 22 9 422 14 9 425 30 9 439 0 9 447 0 10 15 20 10 22 1 10 35 14 10 46 0 10 60 9 10 70 0 10 81 8 10 95 0 10 105 7 10 117 1 10 132 19 10 140 4 10 146 1 10 160 21 10 168 16 10 176 3 10 185 5 10 193 23 10 213 16 10 227 24 10 243 17 10 257 15 10 266 30 10 284 2 10 300 29 10 306 3 10 314 13 10 330 25 10 345 7 10 364 3 10 382 3 10 394 9 10 414 25 10 426 19 10 445 0 10 453 0 11 0 19 11 19 4 11 31 18 11 44 1 11 51 27 11 71 1 11 79 24 11 95 0 11 100 29 11 114 2 11 123 0 11 135 5 11 149 0 11 159 0 11 162 26 11 173 9 11 192 19 11 209 6 11 223 9 11 226 4 11 245 0 11 262 22 11 265 4 11 286 30 11 295 11 11 318 8 11 322 4 11 328 16 11 350 8 11 367 27 11 381 22 11 394 4 11 415 1 11 423 21 11 451 0 11 459 0 12 1 0 12 22 14 12 29 0 12 45 11 12 52 0 12 67 4 12 74 0 12 92 1 12 100 0 12 106 19 12 125 9 12 128 3 12 142 10 12 159 1 12 183 2 12 193 26 12 202 10 12 215 15 12 216 9 12 224 21 12 232 22 12 255 25 12 275 29 12 281 17 12 291 2 12 296 5 12 319 10 12 336 18 12 359 30 12 375 12 12 390 27 12 396 27 12 412 1 12 434 0 12 457 0 12 465 0 13 7 0 13 20 15 13 27 1 13 43 12 13 50 1 13 65 5 13 72 1 13 90 2 13 98 1 13 104 20 13 123 10 13 134 3 13 140 11 13 157 2 13 181 3 13 199 26 13 200 11 13 213 16 13 222 9 13 230 21 13 238 22 13 253 26 13 273 30 13 287 17 13 289 3 13 302 5 13 317 11 13 342 18 13 357 31 13 373 13 13 388 28 13 394 28 13 410 2 13 432 1 13 463 0 13 471 0 14 0 4 14 8 16 14 25 7 14 36 31 14 53 0 14 57 10 14 73 2 14 80 14 14 100 1 14 111 0 14 118 0 14 123 27 14 139 2 14 158 28 14 162 2 14 175 0 14 182 22 14 189 26 14 206 7 14 221 10 14 232 7 14 252 29 14 259 9 14 274 23 14 293 11 14 303 0 14 304 8 14 323 3 14 341 13 14 357 21 14 373 27 14 386 31 14 401 6 14 430 23 14 469 0 14 477 0 15 4 7 15 10 0 15 25 3 15 36 23 15 51 1 15 56 5 15 79 7 15 85 16 15 100 0 15 111 30 15 119 0 15 126 22 15 139 10 15 144 18 15 153 9 15 177 5 15 191 4 15 205 0 15 216 30 15 233 12 15 246 26 15 248 9 15 269 21 15 275 0 15 288 1 15 296 3 15 306 14 15 320 4 15 341 2 15 357 0 15 372 7 15 386 6 15 405 7 15 417 27 15 437 0 15 475 0 16 15 0 16 18 0 16 35 1 16 40 23 16 58 0 16 67 30 16 82 0 16 94 29 16 128 28 16 146 17 16 163 9 16 168 30 16 189 22 16 199 18 16 206 28 16 211 26 16 229 16 16 232 8 16 247 8 16 251 5 16 257 23 16 264 30 16 276 16 16 284 5 16 310 14 16 312 2 16 327 0 16 333 19 16 349 11 16 363 29 16 376 29 16 402 22 16 417 14 16 428 29 16 434 0 16 442 0 17 10 20 17 17 1 17 38 13 17 41 0 17 63 8 17 65 0 17 84 7 17 90 0 17 108 6 17 112 1 17 135 18 17 143 3 17 149 0 17 163 20 17 171 15 17 179 2 17 188 4 17 196 22 17 208 16 17 230 23 17 246 16 17 260 14 17 269 29 17 287 1 17 303 28 17 309 2 17 317 12 17 333 24 17 348 6 17 367 2 17 377 3 17 397 8 17 409 25 17 429 18 17 440 0 17 448 0 18 8 21 18 23 1 18 36 14 18 47 0 18 61 9 18 71 0 18 82 8 18 88 1 18 106 7 18 118 1 18 133 19 18 141 4 18 147 1 18 161 21 18 169 16 18 177 3 18 186 5 18 194 23 18 214 16 18 228 24 18 244 17 18 258 15 18 267 30 18 285 2 18 301 29 18 307 3 18 315 13 18 331 25 18 346 7 18 365 3 18 383 3 18 395 9 18 415 25 18 427 19 18 446 0 18 454 0 19 1 19 19 20 4 19 24 19 19 45 1 19 52 27 19 64 2 19 72 25 19 88 1 19 101 29 19 115 2 19 124 0 19 128 6 19 150 0 19 152 1 19 163 26 19 174 9 19 193 19 19 210 6 19 216 10 19 227 4 19 246 0 19 263 22 19 266 4 19 287 30 19 288 12 19 319 8 19 323 4 19 329 16 19 351 8 19 360 28 19 382 22 19 395 4 19 408 2 19 416 22 19 452 0 19 460 0 20 2 0 20 23 14 20 30 0 20 46 11 20 53 0 20 68 4 20 75 0 20 93 1 20 101 0 20 107 19 20 126 9 20 129 3 20 143 10 20 152 2 20 176 3 20 194 26 20 203 10 20 208 16 20 217 9 20 225 21 20 233 22 20 248 26 20 276 29 20 282 17 20 292 2 20 297 5 20 312 11 20 337 18 20 352 31 20 368 13 20 391 27 20 397 27 20 413 1 20 435 0 20 458 0 20 466 0 21 3 3 21 11 15 21 28 6 21 39 30 21 48 0 21 60 9 21 76 1 21 83 13 21 103 0 21 106 0 21 113 0 21 126 26 21 142 1 21 153 28 21 165 1 21 170 0 21 177 22 21 184 26 21 201 7 21 216 10 21 235 6 21 255 28 21 262 8 21 277 22 21 288 11 21 298 0 21 307 7 21 326 2 21 336 13 21 352 21 21 368 27 21 389 30 21 404 5 21 425 23 21 464 0 21 472 0 22 1 4 22 9 16 22 26 7 22 37 31 22 54 0 22 58 10 22 74 2 22 81 14 22 101 1 22 104 1 22 119 0 22 124 27 22 140 2 22 159 28 22 163 2 22 168 1 22 183 22 22 190 26 22 207 7 22 222 10 22 233 7 22 253 29 22 260 9 22 275 23 22 294 11 22 296 1 22 305 8 22 324 3 22 342 13 22 358 21 22 374 27 22 387 31 22 402 6 22 431 23 22 470 0 22 478 0 23 5 7 23 11 0 23 26 3 23 37 23 23 52 1 23 57 5 23 72 8 23 86 16 23 101 0 23 104 31 23 112 1 23 127 22 23 140 10 23 145 18 23 154 9 23 178 5 23 184 5 23 206 0 23 217 30 23 234 12 23 247 26 23 249 9 23 270 21 23 276 0 23 289 1 23 297 3 23 307 14 23 321 4 23 342 2 23 358 0 23 373 7 23 387 6 23 406 7 23 418 27 23 438 0 23 476 0 24 8 1 24 19 0 24 36 1 24 41 23 24 59 0 24 68 30 24 83 0 24 95 29 24 129 28 24 147 17 24 164 9 24 169 30 24 190 22 24 192 19 24 207 28 24 212 26 24 230 16 24 233 8 24 240 9 24 252 5 24 258 23 24 265 30 24 277 16 24 285 5 24 311 14 24 313 2 24 320 1 24 334 19 24 350 11 24 364 29 24 377 29 24 403 22 24 418 14 24 429 29 24 435 0 24 443 0 25 11 20 25 18 1 25 39 13 25 42 0 25 56 9 25 66 0 25 85 7 25 91 0 25 109 6 25 113 1 25 128 19 25 136 4 25 150 0 25 164 20 25 172 15 25 180 2 25 189 4 25 197 22 25 209 16 25 231 23 25 247 16 25 261 14 25 270 29 25 280 2 25 296 29 25 310 2 25 318 12 25 334 24 25 349 6 25 360 3 25 378 3 25 398 8 25 410 25 25 430 18 25 441 0 25 449 0 26 9 21 26 16 2 26 37 14 26 40 1 26 62 9 26 64 1 26 83 8 26 89 1 26 107 7 26 119 1 26 134 19 26 142 4 26 148 1 26 162 21 26 170 16 26 178 3 26 187 5 26 195 23 26 215 16 26 229 24 26 245 17 26 259 15 26 268 30 26 286 2 26 302 29 26 308 3 26 316 13 26 332 25 26 347 7 26 366 3 26 376 4 26 396 9 26 408 26 26 428 19 26 447 0 26 455 0 27 2 19 27 21 4 27 25 19 27 46 1 27 53 27 27 65 2 27 73 25 27 89 1 27 102 29 27 116 2 27 125 0 27 129 6 27 151 0 27 153 1 27 164 26 27 175 9 27 194 19 27 211 6 27 217 10 27 228 4 27 247 0 27 256 23 27 267 4 27 280 31 27 289 12 27 312 9 27 324 4 27 330 16 27 344 9 27 361 28 27 383 22 27 396 4 27 409 2 27 417 22 27 453 0 27 461 0 28 3 0 28 16 15 28 31 0 28 47 11 28 54 0 28 69 4 28 76 0 28 94 1 28 102 0 28 108 19 28 127 9 28 130 3 28 136 11 28 153 2 28 177 3 28 195 26 28 204 10 28 209 16 28 218 9 28 226 21 28 234 22 28 249 26 28 277 29 28 283 17 28 293 2 28 298 5 28 313 11 28 338 18 28 353 31 28 369 13 28 384 28 28 398 27 28 414 1 28 436 0 28 459 0 28 467 0 29 4 3 29 12 15 29 29 6 29 32 31 29 49 0 29 61 9 29 77 1 29 84 13 29 96 1 29 107 0 29 114 0 29 127 26 29 143 1 29 154 28 29 166 1 29 171 0 29 178 22 29 185 26 29 202 7 29 217 10 29 236 6 29 248 29 29 263 8 29 278 22 29 289 11 29 299 0 29 308 7 29 327 2 29 337 13 29 353 21 29 369 27 29 390 30 29 405 5 29 426 23 29 465 0 29 473 0 30 2 4 30 10 16 30 27 7 30 38 31 30 55 0 30 59 10 30 75 2 30 82 14 30 102 1 30 105 1 30 112 1 30 125 27 30 141 2 30 152 29 30 164 2 30 169 1 30 176 23 30 191 26 30 200 8 30 223 10 30 234 7 30 254 29 30 261 9 30 276 23 30 295 11 30 297 1 30 306 8 30 325 3 30 343 13 30 359 21 30 375 27 30 388 31 30 403 6 30 424 24 30 471 0 30 479 0 31 6 7 31 12 0 31 27 3 31 38 23 31 53 1 31 58 5 31 73 8 31 87 16 31 102 0 31 105 31 31 113 1 31 120 23 31 141 10 31 146 18 31 155 9 31 179 5 31 185 5 31 207 0 31 218 30 31 235 12 31 240 27 31 250 9 31 271 21 31 277 0 31 290 1 31 298 3 31 308 14 31 322 4 31 343 2 31 359 0 31 374 7 31 388 6 31 407 7 31 419 27 31 439 0 31 477 0 32 9 1 32 20 0 32 37 1 32 42 23 32 60 0 32 69 30 32 84 0 32 88 30 32 130 28 32 148 17 32 165 9 32 170 30 32 191 22 32 193 19 32 200 29 32 213 26 32 231 16 32 234 8 32 241 9 32 253 5 32 259 23 32 266 30 32 278 16 32 286 5 32 304 15 32 314 2 32 321 1 32 335 19 32 351 11 32 365 29 32 378 29 32 404 22 32 419 14 32 430 29 32 436 0 32 444 0 33 12 20 33 19 1 33 32 14 33 43 0 33 57 9 33 67 0 33 86 7 33 92 0 33 110 6 33 114 1 33 129 19 33 137 4 33 151 0 33 165 20 33 173 15 33 181 2 33 190 4 33 198 22 33 210 16 33 224 24 33 240 17 33 262 14 33 271 29 33 281 2 33 297 29 33 311 2 33 319 12 33 335 24 33 350 6 33 361 3 33 379 3 33 399 8 33 411 25 33 431 18 33 442 0 33 450 0 34 5 18 34 16 4 34 28 18 34 41 1 34 48 27 34 68 1 34 76 24 34 92 0 34 97 29 34 119 1 34 120 0 34 132 5 34 146 0 34 156 0 34 167 25 34 170 9 34 197 18 34 214 5 34 220 9 34 231 3 34 242 0 34 259 22 34 270 3 34 283 30 34 292 11 34 315 8 34 327 3 34 333 15 34 347 8 34 364 27 34 378 22 34 399 3 34 412 1 34 420 21 34 448 0 34 456 0 35 3 19 35 22 4 35 26 19 35 47 1 35 54 27 35 66 2 35 74 25 35 90 1 35 103 29 35 117 2 35 126 0 35 130 6 35 144 1 35 154 1 35 165 26 35 168 10 35 195 19 35 212 6 35 218 10 35 229 4 35 240 1 35 257 23 35 268 4 35 281 31 35 290 12 35 313 9 35 325 4 35 331 16 35 345 9 35 362 28 35 376 23 35 397 4 35 410 2 35 418 22 35 454 0 35 462 0 36 4 0 36 17 15 36 24 1 36 40 12 36 55 0 36 70 4 36 77 0 36 95 1 36 103 0 36 109 19 36 120 10 36 131 3 36 137 11 36 154 2 36 178 3 36 196 26 36 205 10 36 210 16 36 219 9 36 227 21 36 235 22 36 250 26 36 278 29 36 284 17 36 294 2 36 299 5 36 314 11 36 339 18 36 354 31 36 370 13 36 385 28 36 399 27 36 415 1 36 437 0 36 460 0 36 468 0 37 5 3 37 13 15 37 30 6 37 33 31 37 50 0 37 62 9 37 78 1 37 85 13 37 97 1 37 108 0 37 115 0 37 120 27 37 136 2 37 155 28 37 167 1 37 172 0 37 179 22 37 186 26 37 203 7 37 218 10 37 237 6 37 249 29 37 256 9 37 279 22 37 290 11 37 300 0 37 309 7 37 320 3 37 338 13 37 354 21 37 370 27 37 391 30 37 406 5 37 427 23 37 466 0 37 474 0 38 1 7 38 15 31 38 30 2 38 33 23 38 48 1 38 61 4 38 76 7 38 82 16 38 97 0 38 108 30 38 116 0 38 123 22 38 136 10 38 149 17 38 158 8 38 182 4 38 188 4 38 202 0 38 221 29 38 238 11 38 243 26 38 253 8 38 266 21 38 272 0 38 293 0 38 301 2 38 311 13 38 325 3 38 338 2 38 354 0 38 369 7 38 391 5 38 402 7 38 422 26 38 434 0 38 472 0 39 7 7 39 13 0 39 28 3 39 39 23 39 54 1 39 59 5 39 74 8 39 80 17 39 103 0 39 106 31 39 114 1 39 121 23 39 142 10 39 147 18 39 156 9 39 180 5 39 186 5 39 200 1 39 219 30 39 236 12 39 241 27 39 251 9 39 264 22 39 278 0 39 291 1 39 299 3 39 309 14 39 323 4 39 336 3 39 352 1 39 375 7 39 389 6 39 400 8 39 420 27 39 432 1 39 478 0 40 10 1 40 21 0 40 38 1 40 43 23 40 61 0 40 70 30 40 85 0 40 89 30 40 131 28 40 149 17 40 166 9 40 171 30 40 184 23 40 194 19 40 201 29 40 214 26 40 224 17 40 235 8 40 242 9 40 254 5 40 260 23 40 267 30 40 279 16 40 287 5 40 305 15 40 315 2 40 322 1 40 328 20 40 344 12 40 366 29 40 379 29 40 405 22 40 420 14 40 431 29 40 437 0 40 445 0 41 13 20 41 20 1 41 33 14 41 44 0 41 58 9 41 68 0 41 87 7 41 93 0 41 111 6 41 115 1 41 130 19 41 138 4 41 144 1 41 166 20 41 174 15 41 182 2 41 191 4 41 199 22 41 211 16 41 225 24 41 241 17 41 263 14 41 264 30 41 282 2 41 298 29 41 304 3 41 312 13 41 328 25 41 351 6 41 362 3 41 380 3 41 392 9 41 412 25 41 424 19 41 443 0 41 451 0 42 6 18 42 17 4 42 29 18 42 42 1 42 49 27 42 69 1 42 77 24 42 93 0 42 98 29 42 112 2 42 121 0 42 133 5 42 147 0 42 157 0 42 160 26 42 171 9 42 198 18 42 215 5 42 221 9 42 224 4 42 243 0 42 260 22 42 271 3 42 284 30 42 293 11 42 316 8 42 320 4 42 334 15 42 348 8 42 365 27 42 379 22 42 392 4 42 413 1 42 421 21 42 449 0 42 457 0 43 4 19 43 23 4 43 27 19 43 40 2 43 55 27 43 67 2 43 75 25 43 91 1 43 96 30 43 118 2 43 127 0 43 131 6 43 145 1 43 155 1 43 166 26 43 169 10 43 196 19 43 213 6 43 219 10 43 230 4 43 241 1 43 258 23 43 269 4 43 282 31 43 291 12 43 314 9 43 326 4 43 332 16 43 346 9 43 363 28 43 377 23 43 398 4 43 411 2 43 419 22 43 455 0 43 463 0 44 5 0 44 18 15 44 25 1 44 41 12 44 48 1 44 71 4 44 78 0 44 88 2 44 96 1 44 110 19 44 121 10 44 132 3 44 138 11 44 155 2 44 179 3 44 197 26 44 206 10 44 211 16 44 220 9 44 228 21 44 236 22 44 251 26 44 279 29 44 285 17 44 295 2 44 300 5 44 315 11 44 340 18 44 355 31 44 371 13 44 386 28 44 392 28 44 408 2 44 438 0 44 461 0 44 469 0 45 6 3 45 14 15 45 31 6 45 34 31 45 51 0 45 63 9 45 79 1 45 86 13 45 98 1 45 109 0 45 116 0 45 121 27 45 137 2 45 156 28 45 160 2 45 173 0 45 180 22 45 187 26 45 204 7 45 219 10 45 238 6 45 250 29 45 257 9 45 272 23 45 291 11 45 301 0 45 310 7 45 321 3 45 339 13 45 355 21 45 371 27 45 384 31 45 407 5 45 428 23 45 467 0 45 475 0 46 2 7 46 8 0 46 31 2 46 34 23 46 49 1 46 62 4 46 77 7 46 83 16 46 98 0 46 109 30 46 117 0 46 124 22 46 137 10 46 150 17 46 159 8 46 183 4 46 189 4 46 203 0 46 222 29 46 239 11 46 244 26 46 254 8 46 267 21 46 273 0 46 294 0 46 302 2 46 304 14 46 326 3 46 339 2 46 355 0 46 370 7 46 384 6 46 403 7 46 423 26 46 435 0 46 473 0 47 0 8 47 14 0 47 29 3 47 32 24 47 55 1 47 60 5 47 75 8 47 81 17 47 96 1 47 107 31 47 115 1 47 122 23 47 143 10 47 148 18 47 157 9 47 181 5 47 187 5 47 201 1 47 220 30 47 237 12 47 242 27 47 252 9 47 265 22 47 279 0 47 292 1 47 300 3 47 310 14 47 324 4 47 337 3 47 353 1 47 368 8 47 390 6 47 401 8 47 421 27 47 433 1 47 479 0 

1. A digital communications transmitter employing one or more LDPC codes selected from rates including 1/4, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 13/15, 9/10, wherein the LDPC code with the rate 1/4 has a bit node degree distribution, (b₂,b₃,b₆)=(11264,256,3840), the LDPC code with the rate 2/5 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(8960,256,4608,1536), the LDPC code with the rate 1/2 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(7424,2304,3840,1792), the LDPC code with the rate 3/5 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(5888,3328,4352,1792), the LDPC code with the rate 2/3 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(4864,4096,4864,1536), the LDPC code with the rate 3/4 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(3584,4608,5888,1280), the LDPC code with the rate 4/5 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(2816,5888,5376,1280), the LDPC code with the rate 5/6 has a bit node degree distribution (b₂,b₃,b₄, b₁₀)=(2304,4608,6912,1536), the LDPC code with the rate 13/15 has a bit node degree distribution (b₂,b₃,b₄,b₇)=(1792,5632,6912,1024), and the LDPC code with the rate 9/10 has a bit node degree distribution (b₂,b₃,b₄)=(1280,3584,10496).
 2. A digital communications transmitter employing one or more LDPC codes selected from rates including 1/4, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 13/15, 9/10, wherein the LDPC code of the rate 1/4 is a rate-1/4 LDPC code defined by a parity check matrix expanded from a base matrix B_(1/4), the LDPC code of the rate 2/5 is a rate-2/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(2/5), the LDPC code of the rate 1/2 is a rate-1/2 LDPC code defined by a parity check matrix expanded from a base matrix B_(1/2), the LDPC code of the rate 3/5 is a rate-3/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(3/5), the LDPC code of the rate 2/3 is a rate-2/3 LDPC code defined by a parity check matrix expanded from a base matrix B_(2/5), the LDPC code of the rate 3/4 is a rate-3/4 LDPC code defined by a parity check matrix expanded from a base matrix B_(3/4), the LDPC code of the rate 4/5 is a rate-4/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(4/5), the LDPC code of the rate 5/6 is a rate-5/6 LDPC code defined by a parity check matrix expanded from a base matrix B_(5/6), the LDPC code of the rate 13/15 is a rate-13/15 LDPC code defined by a parity check matrix expanded from a base matrix B_(13/15), and the LDPC code of the rate 9/10 is a rate-9/10 LDPC code defined by a parity check matrix expanded from a base matrix B_(9/10).
 3. A digital communications transmitter employing one or more LDPC codes selected from rates including 1/4, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 13/15, 9/10, wherein the LDPC code of the rate 1/4 is a code equivalent to a rate-1/4 LDPC code defined by a parity check matrix expanded from a base matrix B_(1/4), the LDPC code of the rate 2/5 is a code equivalent to a rate-2/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(2/5), the LDPC code of the rate 1/2 is a code equivalent to a rate-1/2 LDPC code defined by a parity check matrix expanded from a base matrix B_(1/2), the LDPC code of the rate 3/5 is a code equivalent to a rate-3/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(3/5), the LDPC code of the rate 2/3 is a code equivalent to a rate-2/3 LDPC code defined by a parity check matrix expanded from a base matrix B_(2/5), the LDPC code of the rate 3/4 is a code equivalent to a rate-3/4 LDPC code defined by a parity check matrix expanded from a base matrix B_(3/4), the LDPC code of the rate 4/5 is a code equivalent to a rate-4/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(4/5), the LDPC code of the rate 5/6 is a code equivalent to a rate-5/6 LDPC code defined by a parity check matrix expanded from a base matrix B_(5/6), the LDPC code of the rate 13/15 is a code equivalent to a rate-13/15 LDPC code defined by a parity check matrix expanded from a base matrix B_(13/15), and the LDPC code of the rate 9/10 is a code equivalent to a rate-9/10 LDPC code defined by a parity check matrix expanded from a base matrix B_(9/10).
 4. A digital communications receiver employing an LDPC decoder for decoding one or more LDPC codes selected from rates including 1/4, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 13/15, 9/10, wherein the LDPC code with the rate 1/4 has a bit node degree distribution (b₂,b₃,b₆)=(11264,256,3840), the LDPC code with the rate 2/5 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(8960,256,4608,1536), the LDPC code with the rate 1/2 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(7424,2304,3840,1792), the LDPC code with the rate 3/5 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(5888,3328,4352,1792), the LDPC code with the rate 2/3 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(4864,4096,4864,1536), the LDPC code with the rate 3/4 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(3584,4608,5888,1280), the LDPC code with the rate 4/5 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(2816,5888,5376,1280), the LDPC code with the rate 5/6 has a bit node degree distribution (b₂,b₃,b₄,b₁₀)=(2304,4608,6912,1536), the LDPC code with the rate 13/15 has a bit node degree distribution (b₂,b₃,b₄,b₇)=(1792,5632,6912,1024), and the LDPC code with the rate 9/10 has a bit node degree distribution (b₂,b₃,b₄)=(1280,3584,10496).
 5. A digital communications receiver employing an LDPC decoder for decoding one or more LDPC codes selected from rates including 1/4, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 13/15, 9/10, wherein the LDPC code of the rate 1/4 is a rate-1/4 LDPC code defined by a parity check matrix expanded from a base matrix B_(1/4), the LDPC code of the rate 2/5 is a rate-2/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(2/5), the LDPC code of the rate 1/2 is a rate-1/2 LDPC code defined by a parity check matrix expanded from a base matrix B_(1/2), the LDPC code of the rate 3/5 is a rate-3/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(3/5), the LDPC code of the rate 2/3 is a rate-2/3 LDPC code defined by a parity check matrix expanded from a base matrix B_(2/3), the LDPC code of the rate 3/4 is a rate-3/4 LDPC code defined by a parity check matrix expanded from a base matrix B_(3/4), the LDPC code of the rate 4/5 is a rate-4/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(4/5), the LDPC code of the rate 5/6 is a rate-5/6 LDPC code defined by a parity check matrix expanded from a base matrix B_(5/6), the LDPC code of the rate 13/15 is a rate-13/15 LDPC code defined by a parity check matrix expanded from a base matrix B_(13/15), and the LDPC code of the rate 9/10 is a rate-9/10 LDPC code defined by a parity check matrix expanded from a base matrix B_(9/10).
 6. A digital communications receiver employing an LDPC decoder for decoding one or more LDPC codes selected from rates including 1/4, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 13/15, 9/10, wherein the LDPC code of the rate 1/4 is a code equivalent to a rate-1/4 LDPC code defined by a parity check matrix expanded from a base matrix B_(1/4), the LDPC code of the rate 2/5 is a code equivalent to a rate-2/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(2/5), the LDPC code of the rate 1/2 is a code equivalent to a rate-1/2 LDPC code defined by a parity check matrix expanded from a base matrix B_(1/2), the LDPC code of the rate 3/5 is a code equivalent to a rate-3/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(3/5), the LDPC code of the rate 2/3 is a code equivalent to a rate-2/3 LDPC code defined by a parity check matrix expanded from a base matrix B_(2/3), the LDPC code of the rate 3/4 is a code equivalent to a rate-3/4 LDPC code defined by a parity check matrix expanded from a base matrix B_(3/4), the LDPC code of the rate 4/5 is a code equivalent to a rate-4/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(4/5), the LDPC code of the rate 5/6 is a code equivalent to a rate-5/6 LDPC code defined by a parity check matrix expanded from a base matrix B_(5/6), the LDPC code of the rate 13/15 is a code equivalent to a rate-13/15 LDPC code defined by a parity check matrix expanded from a base matrix B_(13/15), and the LDPC code of the rate 9/10 is a code equivalent to a rate-9/10 LDPC code defined by a parity check matrix expanded from a base matrix B_(9/10).
 7. A computer readable medium storing a computer program for performing a method comprising generating one or more LDPC codes selected from rates including 1/4, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 13/15, 9/10, wherein the LDPC code with the rate 1/4 has a bit node degree distribution (b₂,b₃,b₆)=(11264,256,3840), the LDPC code with the rate 2/5 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(8960,256,4608,1536), the LDPC code with the rate 1/2 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(7424,2304,3840,1792), the LDPC code with the rate 3/5 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(5888,3328,4352,1792), the LDPC code with the rate 2/3 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(4864,4096,4864,1536), the LDPC code with the rate 3/4 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(3584,4608,5888,1280), the LDPC code with the rate 4/5 has a bit node degree distribution (b₂,b₃,b₄,b₁₂)=(2816,5888,5376,1280), the LDPC code with the rate 5/6 has a bit node degree distribution (b₂,b₃,b₄,b₁₀)=(2304,4608,6912,1536), the LDPC code with the rate 13/15 has a bit node degree distribution (b₂,b₃,b₄,b₇)=(1792,5632,6912,1024), and LDPC code with the rate 9/10 has a bit node degree distribution (b₂,b₃,b₄)=(1280,3584,10496).
 8. A computer readable medium storing a computer program for performing a method comprising generating one or more LDPC codes selected from rates including 1/4, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 13/15, 9/10, wherein the LDPC code of the rate 1/4 is a rate-1/4 LDPC code defined by a parity check matrix expanded from a base matrix B_(1/4), the LDPC code of the rate 2/5 is a rate-2/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(2/5), the LDPC code of the rate 1/2 is a rate-1/2 LDPC code defined by a parity check matrix expanded from a base matrix B_(1/2), the LDPC code of the rate 3/5 is a rate-3/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(3/5), the LDPC code of the rate 2/3 is a rate-2/3 LDPC code defined by a parity check matrix expanded from a base matrix B_(2/3), the LDPC code of the rate 3/4 is a rate-3/4 LDPC code defined by a parity check matrix expanded from a base matrix B_(3/4), the LDPC code of the rate 4/5 is a rate-4/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(4/5), the LDPC code of the rate 5/6 is a rate-5/6 LDPC code defined by a parity check matrix expanded from a base matrix B_(5/6), the LDPC code of the rate 13/15 is a rate-13/15 LDPC code defined by a parity check matrix expanded from a base matrix B_(13/15), and the LDPC code of the rate 9/10 is a rate-9/10 LDPC code defined by a parity check matrix expanded from a base matrix B_(9/10).
 9. A computer readable medium storing a computer program for performing a method comprising generating one or more LDPC codes selected from rates including 1/4, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 13/15, 9/10, wherein the LDPC code of the rate 1/4 is a code equivalent to a rate-1/4 LDPC code defined by a parity check matrix expanded from a base matrix B_(1/4), the LDPC code of the rate 2/5 is a code equivalent to a rate-2/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(2/5), the LDPC code of the rate 1/2 is a code equivalent to a rate-1/2 LDPC code defined by a parity check matrix expanded from a base matrix B_(1/2), the LDPC code of the rate 3/5 is a code equivalent to a rate-3/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(3/5), the LDPC code of the rate 2/3 is a code equivalent to a rate-2/3 LDPC code defined by a parity check matrix expanded from a base matrix B_(2/3), the LDPC code of the rate 3/4 is a code equivalent to a rate-3/4 LDPC code defined by a parity check matrix expanded from a base matrix B_(3/4), the LDPC code of the rate 4/5 is a code equivalent to a rate-4/5 LDPC code defined by a parity check matrix expanded from a base matrix B_(4/5), the LDPC code of the rate 5/6 is a code equivalent to a rate-5/6 LDPC code defined by a parity check matrix expanded from a base matrix B_(5/6), the LDPC code of the rate 13/15 is a code equivalent to a rate-13/15 LDPC code defined by a parity check matrix expanded from a base matrix B_(13/15), and the LDPC code of the rate 9/10 is a code equivalent to a rate-9/10 LDPC code defined by a parity check matrix expanded from a base matrix B_(9/10). 